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    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_019e415a-4e63-7ba0-8205-b9102357db83_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average ordinary shares outstanding:</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_019e415a-4e63-7bf5-b571-6e335f0b7061_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember"/>
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    <link:label id="lab_srt_RangeMember_019e415a-4dba-7d49-a03d-e8d44522d8c8_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputAssetFreezeMember_019e415a-4dba-756d-a4f0-80c3bb04eda8_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputAssetFreezeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset freeze</link:label>
    <link:label id="lab_bur_MeasurementInputAssetFreezeMember_label_en-US" xlink:label="lab_bur_MeasurementInputAssetFreezeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Asset Freeze [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputAssetFreezeMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputAssetFreezeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using asset freeze.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputAssetFreezeMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputAssetFreezeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputAssetFreezeMember" xlink:to="lab_bur_MeasurementInputAssetFreezeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueIssuedForServices_019fa9f6-e704-7d30-88c3-c7ac6a134a89_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueIssuedForServices" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of new ordinary shares under the NED Plan</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueIssuedForServices_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueIssuedForServices" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Issued for Services</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueIssuedForServices" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueIssuedForServices"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueIssuedForServices" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueIssuedForServices" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_019e415a-4dba-74ce-b4e4-86f06194e377_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_TreasuryStockCommonSharesCost_019e415a-4dba-7d6b-a309-dcddc11e6779_terseLabel_en-US" xlink:label="lab_bur_TreasuryStockCommonSharesCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury shares per share (in dollars per share)</link:label>
    <link:label id="lab_bur_TreasuryStockCommonSharesCost_label_en-US" xlink:label="lab_bur_TreasuryStockCommonSharesCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock Common Shares, Cost</link:label>
    <link:label id="lab_bur_TreasuryStockCommonSharesCost_documentation_en-US" xlink:label="lab_bur_TreasuryStockCommonSharesCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Per share price of treasury shares common stock.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_TreasuryStockCommonSharesCost" xlink:href="bur-20260630.xsd#bur_TreasuryStockCommonSharesCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_TreasuryStockCommonSharesCost" xlink:to="lab_bur_TreasuryStockCommonSharesCost" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019e415a-4dba-76d8-a15a-4c7799f15bb3_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019e415a-4dba-7f73-a07a-ee09c415de4c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_CapitalProvisionIncomeLossMember_019e415a-4e63-7950-9c25-5a164c89f0c5_terseLabel_en-US" xlink:label="lab_bur_CapitalProvisionIncomeLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital provision income/(loss)</link:label>
    <link:label id="lab_bur_CapitalProvisionIncomeLossMember_label_en-US" xlink:label="lab_bur_CapitalProvisionIncomeLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Provision Income (Loss) [Member]</link:label>
    <link:label id="lab_bur_CapitalProvisionIncomeLossMember_documentation_en-US" xlink:label="lab_bur_CapitalProvisionIncomeLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents information pertaining to capital provision income.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_CapitalProvisionIncomeLossMember" xlink:href="bur-20260630.xsd#bur_CapitalProvisionIncomeLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_CapitalProvisionIncomeLossMember" xlink:to="lab_bur_CapitalProvisionIncomeLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract_019e415a-4dba-702a-88cb-8e241bd220bc_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Liabilities Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:to="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_019e415a-4e63-7550-9f77-a811687e6699_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ordinary shares, no par value; unlimited shares authorized; 221,829,450 ordinary shares issued and 219,584,503 ordinary shares outstanding as of June&#160;30, 2026 and 220,667,387 ordinary shares issued and 218,897,440 ordinary shares outstanding as of December&#160;31, 2025</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesTransfersBetweenLevels_019e415a-4e63-728c-9792-a4d8e368dadf_terseLabel_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesTransfersBetweenLevels" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers between types</link:label>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesTransfersBetweenLevels_label_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesTransfersBetweenLevels" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Liabilities, Transfers Between Levels</link:label>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesTransfersBetweenLevels_documentation_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesTransfersBetweenLevels" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Liabilities, Transfers Between Levels</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesTransfersBetweenLevels" xlink:href="bur-20260630.xsd#bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesTransfersBetweenLevels"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesTransfersBetweenLevels" xlink:to="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesTransfersBetweenLevels" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ChangeInExpectedTimingAxis_019e415a-4dba-755c-bbb0-528ba12b8b15_terseLabel_en-US" xlink:label="lab_bur_ChangeInExpectedTimingAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change In Expected Timing [Axis]</link:label>
    <link:label id="lab_bur_ChangeInExpectedTimingAxis_label_en-US" xlink:label="lab_bur_ChangeInExpectedTimingAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change In Expected Timing [Axis]</link:label>
    <link:label id="lab_bur_ChangeInExpectedTimingAxis_documentation_en-US" xlink:label="lab_bur_ChangeInExpectedTimingAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Change In Expected Timing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ChangeInExpectedTimingAxis" xlink:href="bur-20260630.xsd#bur_ChangeInExpectedTimingAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ChangeInExpectedTimingAxis" xlink:to="lab_bur_ChangeInExpectedTimingAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_019e415a-4e63-7df7-b2c4-eeba5ce97a6d_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_019e415a-4dba-7aa7-891b-dbebfdc6271d_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019e415a-4e64-7416-9361-6159272b0be8_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_019e415a-4e63-72f4-9654-51c9a5cb1f5c_terseLabel_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset-backed securities</link:label>
    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset-Backed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetBackedSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetBackedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetBackedSecuritiesMember" xlink:to="lab_us-gaap_AssetBackedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_CapitalProvisionAssetsAbstract_019e415a-4dba-77b5-b95b-fca63abe314a_terseLabel_en-US" xlink:label="lab_bur_CapitalProvisionAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital provision assets</link:label>
    <link:label id="lab_bur_CapitalProvisionAssetsAbstract_label_en-US" xlink:label="lab_bur_CapitalProvisionAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Provision Assets [Abstract]</link:label>
    <link:label id="lab_bur_CapitalProvisionAssetsAbstract_documentation_en-US" xlink:label="lab_bur_CapitalProvisionAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">No definition available.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_CapitalProvisionAssetsAbstract" xlink:href="bur-20260630.xsd#bur_CapitalProvisionAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_CapitalProvisionAssetsAbstract" xlink:to="lab_bur_CapitalProvisionAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueProceedsReceived_019e415a-4dba-785a-a2f1-7f0c84606168_negatedTerseLabel_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueProceedsReceived" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from capital provision assets</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueProceedsReceived_label_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueProceedsReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Held At Fair Value, Proceeds Received</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueProceedsReceived_documentation_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueProceedsReceived" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds from capital provision assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccountsReceivableHeldAtFairValueProceedsReceived" xlink:href="bur-20260630.xsd#bur_AccountsReceivableHeldAtFairValueProceedsReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccountsReceivableHeldAtFairValueProceedsReceived" xlink:to="lab_bur_AccountsReceivableHeldAtFairValueProceedsReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsForeignExchangeGainsLosses_019e415a-4e63-7889-9c53-2fe1bfaf3330_terseLabel_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsForeignExchangeGainsLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange gains/(losses)</link:label>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsForeignExchangeGainsLosses_label_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsForeignExchangeGainsLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Assets, Foreign Exchange Gains (Losses)</link:label>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsForeignExchangeGainsLosses_documentation_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsForeignExchangeGainsLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of foreign exchange gains/(losses) recognized from asset measured at fair value on recurring basis using unobservable input (level 3).</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsForeignExchangeGainsLosses" xlink:href="bur-20260630.xsd#bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsForeignExchangeGainsLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsForeignExchangeGainsLosses" xlink:to="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsForeignExchangeGainsLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputSignificantPositiveRulingOrOtherObjectiveEventPriorToTrialCourtJudgmentMember_019e415a-4e63-71ff-8c52-62999a333903_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputSignificantPositiveRulingOrOtherObjectiveEventPriorToTrialCourtJudgmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant ruling or other objective event prior to trial court judgment</link:label>
    <link:label id="lab_bur_MeasurementInputSignificantPositiveRulingOrOtherObjectiveEventPriorToTrialCourtJudgmentMember_label_en-US" xlink:label="lab_bur_MeasurementInputSignificantPositiveRulingOrOtherObjectiveEventPriorToTrialCourtJudgmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Significant Positive Ruling Or Other Objective Event Prior To Trial Court Judgment [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputSignificantPositiveRulingOrOtherObjectiveEventPriorToTrialCourtJudgmentMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputSignificantPositiveRulingOrOtherObjectiveEventPriorToTrialCourtJudgmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using significant positive ruling or other objective event prior to any trial court judgment.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputSignificantPositiveRulingOrOtherObjectiveEventPriorToTrialCourtJudgmentMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputSignificantPositiveRulingOrOtherObjectiveEventPriorToTrialCourtJudgmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputSignificantPositiveRulingOrOtherObjectiveEventPriorToTrialCourtJudgmentMember" xlink:to="lab_bur_MeasurementInputSignificantPositiveRulingOrOtherObjectiveEventPriorToTrialCourtJudgmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtRollingMaturityAbstract_019e415a-4dba-7bd4-8221-55e280428d33_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtRollingMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt payable</link:label>
    <link:label id="lab_us-gaap_LongTermDebtRollingMaturityAbstract_label_en-US" xlink:label="lab_us-gaap_LongTermDebtRollingMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Rolling Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtRollingMaturityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtRollingMaturityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtRollingMaturityAbstract" xlink:to="lab_us-gaap_LongTermDebtRollingMaturityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_019e415a-4e63-7f43-880e-00da1cec5dfe_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019e415a-4dba-7d35-9585-a01ec822f4b5_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transactions</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccountsReceivableMeasurementInput_019e415a-4dba-7c93-b88e-dcf8ceb3f78d_terseLabel_en-US" xlink:label="lab_bur_AccountsReceivableMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from settlement of capital provision assets, measurement input</link:label>
    <link:label id="lab_bur_AccountsReceivableMeasurementInput_label_en-US" xlink:label="lab_bur_AccountsReceivableMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Measurement Input</link:label>
    <link:label id="lab_bur_AccountsReceivableMeasurementInput_documentation_en-US" xlink:label="lab_bur_AccountsReceivableMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccountsReceivableMeasurementInput" xlink:href="bur-20260630.xsd#bur_AccountsReceivableMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccountsReceivableMeasurementInput" xlink:to="lab_bur_AccountsReceivableMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_019e415a-4dba-7b40-abb0-7f18f4907405_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers into Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Transfers Into Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputExhaustionOfAsOfRightAppealsMember_019e415a-4e63-75e5-a427-9c12c1a6b853_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputExhaustionOfAsOfRightAppealsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exhaustion of as-of-right appeals</link:label>
    <link:label id="lab_bur_MeasurementInputExhaustionOfAsOfRightAppealsMember_label_en-US" xlink:label="lab_bur_MeasurementInputExhaustionOfAsOfRightAppealsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Exhaustion Of As-Of-Right Appeals [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputExhaustionOfAsOfRightAppealsMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputExhaustionOfAsOfRightAppealsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Exhaustion Of As-Of-Right Appeals</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputExhaustionOfAsOfRightAppealsMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputExhaustionOfAsOfRightAppealsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputExhaustionOfAsOfRightAppealsMember" xlink:to="lab_bur_MeasurementInputExhaustionOfAsOfRightAppealsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_PaymentsToAcquireInterestInJointVenturesAndEquityMethodInvestment_019e415a-4e63-728e-9801-6af495ad06bd_terseLabel_en-US" xlink:label="lab_bur_PaymentsToAcquireInterestInJointVenturesAndEquityMethodInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fundings of joint ventures and equity method investments</link:label>
    <link:label id="lab_bur_PaymentsToAcquireInterestInJointVenturesAndEquityMethodInvestment_label_en-US" xlink:label="lab_bur_PaymentsToAcquireInterestInJointVenturesAndEquityMethodInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments To Acquire Interest In Joint Ventures And Equity Method Investment</link:label>
    <link:label id="lab_bur_PaymentsToAcquireInterestInJointVenturesAndEquityMethodInvestment_documentation_en-US" xlink:label="lab_bur_PaymentsToAcquireInterestInJointVenturesAndEquityMethodInvestment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The cash outflow from investment in joint ventures and equity method investments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_PaymentsToAcquireInterestInJointVenturesAndEquityMethodInvestment" xlink:href="bur-20260630.xsd#bur_PaymentsToAcquireInterestInJointVenturesAndEquityMethodInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_PaymentsToAcquireInterestInJointVenturesAndEquityMethodInvestment" xlink:to="lab_bur_PaymentsToAcquireInterestInJointVenturesAndEquityMethodInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_019e415a-4e64-7f53-b494-7f5a35eaaaeb_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_019e415a-4dba-7fd0-8e89-1bb9cc1a7e80_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_PrincipalFinanceSegmentMember_019e415a-4e63-7da7-a078-edc76043cca7_terseLabel_en-US" xlink:label="lab_bur_PrincipalFinanceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal Finance</link:label>
    <link:label id="lab_bur_PrincipalFinanceSegmentMember_label_en-US" xlink:label="lab_bur_PrincipalFinanceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Principal Finance Segment [Member]</link:label>
    <link:label id="lab_bur_PrincipalFinanceSegmentMember_documentation_en-US" xlink:label="lab_bur_PrincipalFinanceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Principal Finance Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_PrincipalFinanceSegmentMember" xlink:href="bur-20260630.xsd#bur_PrincipalFinanceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_PrincipalFinanceSegmentMember" xlink:to="lab_bur_PrincipalFinanceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_PaymentsForProceedsFromMarketableSecurities_019e415a-4e63-7a6a-954e-edb6f3215941_negatedLabel_en-US" xlink:label="lab_bur_PaymentsForProceedsFromMarketableSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net proceeds from/(funding of) marketable securities</link:label>
    <link:label id="lab_bur_PaymentsForProceedsFromMarketableSecurities_label_en-US" xlink:label="lab_bur_PaymentsForProceedsFromMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For (Proceeds From) Marketable Securities</link:label>
    <link:label id="lab_bur_PaymentsForProceedsFromMarketableSecurities_documentation_en-US" xlink:label="lab_bur_PaymentsForProceedsFromMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The net cash inflow or outflow from marketable securities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_PaymentsForProceedsFromMarketableSecurities" xlink:href="bur-20260630.xsd#bur_PaymentsForProceedsFromMarketableSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_PaymentsForProceedsFromMarketableSecurities" xlink:to="lab_bur_PaymentsForProceedsFromMarketableSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019e415a-4dba-7ae8-839d-1a87cf0507b1_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DebtInstrumentRedemptionPriceChangeInControlPercentage_019e415a-4dba-71e3-a5b4-6ee301f62524_terseLabel_en-US" xlink:label="lab_bur_DebtInstrumentRedemptionPriceChangeInControlPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption price, change in control, percentage</link:label>
    <link:label id="lab_bur_DebtInstrumentRedemptionPriceChangeInControlPercentage_label_en-US" xlink:label="lab_bur_DebtInstrumentRedemptionPriceChangeInControlPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Change In Control, Percentage</link:label>
    <link:label id="lab_bur_DebtInstrumentRedemptionPriceChangeInControlPercentage_documentation_en-US" xlink:label="lab_bur_DebtInstrumentRedemptionPriceChangeInControlPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Change In Control, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DebtInstrumentRedemptionPriceChangeInControlPercentage" xlink:href="bur-20260630.xsd#bur_DebtInstrumentRedemptionPriceChangeInControlPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DebtInstrumentRedemptionPriceChangeInControlPercentage" xlink:to="lab_bur_DebtInstrumentRedemptionPriceChangeInControlPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedInsuranceCurrentAndNoncurrent_019e415a-4dba-7824-884f-6886971a8352_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedInsuranceCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedInsuranceCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccruedInsuranceCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Insurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedInsuranceCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedInsuranceCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedInsuranceCurrentAndNoncurrent" xlink:to="lab_us-gaap_AccruedInsuranceCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_019e415a-4e63-74ce-a568-7e4543d6422a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fundings and Proceeds from Joint Ventures and Equity Method Investments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_CapitalProvisionUndrawnCommitments_019e415a-4e63-73e0-9018-52d2ce7265b5_totalLabel_en-US" xlink:label="lab_bur_CapitalProvisionUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total capital provision undrawn commitments</link:label>
    <link:label id="lab_bur_CapitalProvisionUndrawnCommitments_label_en-US" xlink:label="lab_bur_CapitalProvisionUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Provision Undrawn Commitments</link:label>
    <link:label id="lab_bur_CapitalProvisionUndrawnCommitments_documentation_en-US" xlink:label="lab_bur_CapitalProvisionUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The amount of capital provision undrawn commitments as at the end of the reporting period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_CapitalProvisionUndrawnCommitments" xlink:href="bur-20260630.xsd#bur_CapitalProvisionUndrawnCommitments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_CapitalProvisionUndrawnCommitments" xlink:to="lab_bur_CapitalProvisionUndrawnCommitments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_019e415a-4dba-7605-b920-9b64b14cdea3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromOtherOperatingActivities_019e415a-4e63-7e6c-8b6f-6aaf13e5849f_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromOtherOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from/(payments of) other income</link:label>
    <link:label id="lab_us-gaap_ProceedsFromOtherOperatingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromOtherOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Other Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromOtherOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromOtherOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromOtherOperatingActivities" xlink:to="lab_us-gaap_ProceedsFromOtherOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019e415a-4e63-7d77-9b8e-75afa538e0ef_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearFive_019e415a-4dba-7cd2-afdd-5a03fe44087e_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments of Principal in Rolling Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetLossJudgmentReversal_019e415a-4dba-7a30-878b-c11f954488f8_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetLossJudgmentReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital provision loss</link:label>
    <link:label id="lab_bur_DerivativeAssetLossJudgmentReversal_label_en-US" xlink:label="lab_bur_DerivativeAssetLossJudgmentReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset Loss, Judgment Reversal</link:label>
    <link:label id="lab_bur_DerivativeAssetLossJudgmentReversal_documentation_en-US" xlink:label="lab_bur_DerivativeAssetLossJudgmentReversal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Asset Loss, Judgment Reversal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetLossJudgmentReversal" xlink:href="bur-20260630.xsd#bur_DerivativeAssetLossJudgmentReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetLossJudgmentReversal" xlink:to="lab_bur_DerivativeAssetLossJudgmentReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingAfterYearFive_019e415a-4dba-7542-a4a4-3c48c1b039f7_terseLabel_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingAfterYearFive_label_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Rolling After Year Five</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingAfterYearFive_documentation_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Rolling After Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingAfterYearFive" xlink:href="bur-20260630.xsd#bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingAfterYearFive" xlink:to="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock_019e415a-4dba-7b60-b516-919d544e8d09_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation of Capital Provision Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Assets at Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_019e415a-4e63-7f7e-805b-d947b84ae35f_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTable" xlink:to="lab_us-gaap_ConcentrationRiskTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019e415a-4e63-7d40-a205-9959b5959fd2_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_CompanyAndRestrictedSubsidiaryMember_019e415a-4dba-740a-b87d-44454f3790cf_terseLabel_en-US" xlink:label="lab_bur_CompanyAndRestrictedSubsidiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company and its Restricted Subsidiaries</link:label>
    <link:label id="lab_bur_CompanyAndRestrictedSubsidiaryMember_label_en-US" xlink:label="lab_bur_CompanyAndRestrictedSubsidiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company And Restricted Subsidiary [Member]</link:label>
    <link:label id="lab_bur_CompanyAndRestrictedSubsidiaryMember_documentation_en-US" xlink:label="lab_bur_CompanyAndRestrictedSubsidiaryMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to Company and its restricted subsidiaries.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_CompanyAndRestrictedSubsidiaryMember" xlink:href="bur-20260630.xsd#bur_CompanyAndRestrictedSubsidiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_CompanyAndRestrictedSubsidiaryMember" xlink:to="lab_bur_CompanyAndRestrictedSubsidiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AssetsLiabilitiesNetCost_019e415a-4e63-75ad-9c8b-e50f268e2117_terseLabel_en-US" xlink:label="lab_bur_AssetsLiabilitiesNetCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset (liability) cost</link:label>
    <link:label id="lab_bur_AssetsLiabilitiesNetCost_label_en-US" xlink:label="lab_bur_AssetsLiabilitiesNetCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets (Liabilities) Net, Cost</link:label>
    <link:label id="lab_bur_AssetsLiabilitiesNetCost_documentation_en-US" xlink:label="lab_bur_AssetsLiabilitiesNetCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of assets liabilities net at cost.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AssetsLiabilitiesNetCost" xlink:href="bur-20260630.xsd#bur_AssetsLiabilitiesNetCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AssetsLiabilitiesNetCost" xlink:to="lab_bur_AssetsLiabilitiesNetCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_019e415a-4e63-7071-9aea-8462a63260ef_terseLabel_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from settlement of capital provision assets</link:label>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans, Notes, Trade and Other Receivables Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:to="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesAbstract_label_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivablesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesAbstract" xlink:to="lab_us-gaap_ReceivablesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019e415a-4e63-70b3-a43d-2e2456c7fd0b_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfOrdinaryDividends_019ef0ef-8b74-7e43-b0dc-266fca7ea0e4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on ordinary shares</link:label>
    <link:label id="lab_us-gaap_PaymentsOfOrdinaryDividends_label_en-US" xlink:label="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfOrdinaryDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfOrdinaryDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfOrdinaryDividends" xlink:to="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalCashFlowElementsAndSupplementalCashFlowInformationAbstract_019e415a-4dba-7846-9946-c6bf25cf0344_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalCashFlowElementsAndSupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows</link:label>
    <link:label id="lab_us-gaap_AdditionalCashFlowElementsAndSupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_AdditionalCashFlowElementsAndSupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Cash Flow Elements and Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalCashFlowElementsAndSupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalCashFlowElementsAndSupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalCashFlowElementsAndSupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_AdditionalCashFlowElementsAndSupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019e415a-4dba-7c3c-a5b0-b5a1e7361607_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesMeasurementInput_019e415a-4e63-7eae-8170-466177b4d8fe_terseLabel_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets of consolidated investment companies, measurement input</link:label>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesMeasurementInput_label_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Of Consolidated Investment Companies, Measurement Input</link:label>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesMeasurementInput_documentation_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets Of Consolidated Investment Companies, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AssetsOfConsolidatedInvestmentCompaniesMeasurementInput" xlink:href="bur-20260630.xsd#bur_AssetsOfConsolidatedInvestmentCompaniesMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AssetsOfConsolidatedInvestmentCompaniesMeasurementInput" xlink:to="lab_bur_AssetsOfConsolidatedInvestmentCompaniesMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsCost_019e415a-4dba-7bad-bcb0-ba107c1ae2af_verboseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsCost" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Capital provision assets, Cost</link:label>
    <link:label id="lab_bur_DerivativeAssetsCost_label_en-US" xlink:label="lab_bur_DerivativeAssetsCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets, Cost</link:label>
    <link:label id="lab_bur_DerivativeAssetsCost_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital provision assets at cost.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsCost" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsCost" xlink:to="lab_bur_DerivativeAssetsCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_019e415a-4e63-7c6c-8cf4-57da47dfbbec_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of new ordinary shares to satisfy vested share-based awards (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Restricted Stock Award, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_019e415a-4e63-7221-b4bc-3e3b889c7b4d_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FairValueAdjustmentsAxis_019e415a-4dba-7c8d-989e-6e2743b98450_terseLabel_en-US" xlink:label="lab_bur_FairValueAdjustmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Adjustments [Axis]</link:label>
    <link:label id="lab_bur_FairValueAdjustmentsAxis_label_en-US" xlink:label="lab_bur_FairValueAdjustmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Adjustments [Axis]</link:label>
    <link:label id="lab_bur_FairValueAdjustmentsAxis_documentation_en-US" xlink:label="lab_bur_FairValueAdjustmentsAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Information by fair value adjustment.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FairValueAdjustmentsAxis" xlink:href="bur-20260630.xsd#bur_FairValueAdjustmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FairValueAdjustmentsAxis" xlink:to="lab_bur_FairValueAdjustmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019e415a-4e63-743c-a658-4226a9e3b161_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_IncomeLossOnDerivativeAssets_019e415a-4e63-73da-9c25-fd4a88ba793e_verboseLabel_en-US" xlink:label="lab_bur_IncomeLossOnDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) for the period</link:label>
    <link:label id="lab_bur_IncomeLossOnDerivativeAssets_019e415a-4e63-717a-ab34-bd8cbcfa26bb_totalLabel_en-US" xlink:label="lab_bur_IncomeLossOnDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) on capital provision assets</link:label>
    <link:label id="lab_bur_IncomeLossOnDerivativeAssets_label_en-US" xlink:label="lab_bur_IncomeLossOnDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) On Derivative Assets</link:label>
    <link:label id="lab_bur_IncomeLossOnDerivativeAssets_documentation_en-US" xlink:label="lab_bur_IncomeLossOnDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income (Loss) On Derivative Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_IncomeLossOnDerivativeAssets" xlink:href="bur-20260630.xsd#bur_IncomeLossOnDerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_IncomeLossOnDerivativeAssets" xlink:to="lab_bur_IncomeLossOnDerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019e415a-4e63-74e2-bbb6-f6f777be334b_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recently issued or adopted accounting pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersIntoLevel3_019e415a-4e63-78a6-a21c-075748f7e2dc_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers into Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersIntoLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Liability, Transfers Into Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersIntoLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersIntoLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersIntoLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersIntoLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019e415a-4dba-7303-8e89-1400d2a3096b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reportable Business Segments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_019e415a-4e63-7775-bd87-54261a1d3172_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-controlling interests</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestMember" xlink:to="lab_us-gaap_NoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_019e415a-4dba-7388-a725-cbf39f619ea3_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs incurred as finance costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_019e415a-4dba-73ad-9479-6a711ab3e5a4_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019e415a-4dba-7835-b531-d6d0b35c7e54_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ChangeInInterestRateDomain_019e415a-4dba-77de-a243-445355ec594e_terseLabel_en-US" xlink:label="lab_bur_ChangeInInterestRateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change In Interest Rate [Domain]</link:label>
    <link:label id="lab_bur_ChangeInInterestRateDomain_label_en-US" xlink:label="lab_bur_ChangeInInterestRateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change In Interest Rate [Domain]</link:label>
    <link:label id="lab_bur_ChangeInInterestRateDomain_documentation_en-US" xlink:label="lab_bur_ChangeInInterestRateDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Change In Interest Rate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ChangeInInterestRateDomain" xlink:href="bur-20260630.xsd#bur_ChangeInInterestRateDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ChangeInInterestRateDomain" xlink:to="lab_bur_ChangeInInterestRateDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_019e415a-4e63-7c7a-ac67-cea77539a004_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt payable</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019e415a-4e63-7131-b3a9-134517c8082a_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Carrying value (at amortized cost) as of</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019e415a-4e63-701c-a4d3-d6933e919656_netLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Third-party indebtedness</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesAbstract_019e415a-4dba-78cd-b3b9-5c09eefe048b_terseLabel_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets of consolidated investment companies</link:label>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesAbstract_label_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Of Consolidated Investment Companies [Abstract]</link:label>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesAbstract_documentation_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets Of Consolidated Investment Companies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AssetsOfConsolidatedInvestmentCompaniesAbstract" xlink:href="bur-20260630.xsd#bur_AssetsOfConsolidatedInvestmentCompaniesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AssetsOfConsolidatedInvestmentCompaniesAbstract" xlink:to="lab_bur_AssetsOfConsolidatedInvestmentCompaniesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ScheduleOfTotalAssetsThirdPartiesIndebtednessAndRevenuesTableTextBlock_019e415a-4dba-7d90-80fd-7ab2a8bb1ce4_terseLabel_en-US" xlink:label="lab_bur_ScheduleOfTotalAssetsThirdPartiesIndebtednessAndRevenuesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Total Assets, Third-party Indebtedness and Revenues</link:label>
    <link:label id="lab_bur_ScheduleOfTotalAssetsThirdPartiesIndebtednessAndRevenuesTableTextBlock_label_en-US" xlink:label="lab_bur_ScheduleOfTotalAssetsThirdPartiesIndebtednessAndRevenuesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Total Assets Third Parties Indebtedness And Revenues [Table Text Block]</link:label>
    <link:label id="lab_bur_ScheduleOfTotalAssetsThirdPartiesIndebtednessAndRevenuesTableTextBlock_documentation_en-US" xlink:label="lab_bur_ScheduleOfTotalAssetsThirdPartiesIndebtednessAndRevenuesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tabular disclosure of total assets, third party indebtedness and revenues pursuant to the indentures governing the 2028 Notes, the 2030 Notes and the 2031</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ScheduleOfTotalAssetsThirdPartiesIndebtednessAndRevenuesTableTextBlock" xlink:href="bur-20260630.xsd#bur_ScheduleOfTotalAssetsThirdPartiesIndebtednessAndRevenuesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ScheduleOfTotalAssetsThirdPartiesIndebtednessAndRevenuesTableTextBlock" xlink:to="lab_bur_ScheduleOfTotalAssetsThirdPartiesIndebtednessAndRevenuesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ProceedsFromDerivativeAssets_019e415a-4dba-77ab-96d2-3416454be722_terseLabel_en-US" xlink:label="lab_bur_ProceedsFromDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from capital provision assets</link:label>
    <link:label id="lab_bur_ProceedsFromDerivativeAssets_label_en-US" xlink:label="lab_bur_ProceedsFromDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Derivative Assets</link:label>
    <link:label id="lab_bur_ProceedsFromDerivativeAssets_documentation_en-US" xlink:label="lab_bur_ProceedsFromDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Derivative Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ProceedsFromDerivativeAssets" xlink:href="bur-20260630.xsd#bur_ProceedsFromDerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ProceedsFromDerivativeAssets" xlink:to="lab_bur_ProceedsFromDerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_019e415a-4dba-7917-91ac-10e831afa123_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_019e415a-4dba-7f67-af5e-4baac9eea043_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccruedBonusesPayments_019e415a-4dba-7c4a-9cc9-e65078323b81_negatedLabel_en-US" xlink:label="lab_bur_AccruedBonusesPayments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Cash paid</link:label>
    <link:label id="lab_bur_AccruedBonusesPayments_label_en-US" xlink:label="lab_bur_AccruedBonusesPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Bonuses, Payments</link:label>
    <link:label id="lab_bur_AccruedBonusesPayments_documentation_en-US" xlink:label="lab_bur_AccruedBonusesPayments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of cash paid during the year for long term incentive compensation.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccruedBonusesPayments" xlink:href="bur-20260630.xsd#bur_AccruedBonusesPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccruedBonusesPayments" xlink:to="lab_bur_AccruedBonusesPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e415a-4e63-7f1d-999e-7d2cede71d20_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by/(used in) investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CompensationExpenseExcludingCostOfGoodAndServiceSold_019e415a-4e63-7a24-be5c-6d5bbc45e294_terseLabel_en-US" xlink:label="lab_us-gaap_CompensationExpenseExcludingCostOfGoodAndServiceSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Annual incentive compensation</link:label>
    <link:label id="lab_us-gaap_CompensationExpenseExcludingCostOfGoodAndServiceSold_label_en-US" xlink:label="lab_us-gaap_CompensationExpenseExcludingCostOfGoodAndServiceSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Expense, Excluding Cost of Good and Service Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CompensationExpenseExcludingCostOfGoodAndServiceSold" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CompensationExpenseExcludingCostOfGoodAndServiceSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CompensationExpenseExcludingCostOfGoodAndServiceSold" xlink:to="lab_us-gaap_CompensationExpenseExcludingCostOfGoodAndServiceSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019e415a-4dba-7d49-873f-0816f9efc0ce_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Principal value</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_019e415a-4dba-7da9-96b9-b34f836b4430_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to Burford Capital Limited shareholders per ordinary share:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:to="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019e415a-4dba-7c67-a3ee-521b45272771_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shareholders' equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019e415a-4e63-78b9-b258-7599067495c5_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_019e415a-4dba-78a2-9d3f-18fbb6ec6c49_negatedLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Treasury shares; 2,244,947 ordinary shares at $12.71 cost as of June&#160;30, 2026 and 1,769,947 ordinary shares at $14.06 cost as of December&#160;31, 2025</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonValue" xlink:to="lab_us-gaap_TreasuryStockCommonValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019e415a-4dba-76a5-af1e-44e44988118e_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_019e415a-4dba-70f7-a98a-9c16bfe158f1_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetSales_019e415a-4e63-7049-996f-cf366db3df6f_negatedLabel_en-US" xlink:label="lab_bur_DerivativeAssetSales" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Realizations</link:label>
    <link:label id="lab_bur_DerivativeAssetSales_label_en-US" xlink:label="lab_bur_DerivativeAssetSales" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Sales</link:label>
    <link:label id="lab_bur_DerivativeAssetSales_documentation_en-US" xlink:label="lab_bur_DerivativeAssetSales" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital provision assets realizations during the period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetSales" xlink:href="bur-20260630.xsd#bur_DerivativeAssetSales"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetSales" xlink:to="lab_bur_DerivativeAssetSales" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019e415a-4e63-7ce3-80ed-bb7ce209eccc_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income/(loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019e415a-4e63-7d74-9ccb-dd8eae2732d1_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_019e415a-4dba-73c1-8d2c-ce89aaff713c_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_019e415a-4e63-7565-8d89-fccdab22d098_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) for the period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearThree_019e415a-4e63-7e6f-b53f-42308a882f32_terseLabel_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearThree_label_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Rolling Year Three</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearThree_documentation_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Rolling Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearThree" xlink:href="bur-20260630.xsd#bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearThree" xlink:to="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_019fa9f6-af5a-7cba-8811-48a31c0a95ba_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of new ordinary shares under the NED Plan (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Issued for Services</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesIssuedForServices"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_019e415a-4e63-7dd3-8a8e-18c4e039f0b2_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per ordinary share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019e415a-4dba-73bc-a431-ddbeeda0e571_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to Burford Capital Limited shareholders per ordinary share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019e415a-4dba-7322-bf12-17e1459e21e8_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_PositiveFairValueAdjustmentsMember_019e415a-4e63-7a87-ae47-7ef011d3828c_terseLabel_en-US" xlink:label="lab_bur_PositiveFairValueAdjustmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Positive case milestone factor:</link:label>
    <link:label id="lab_bur_PositiveFairValueAdjustmentsMember_label_en-US" xlink:label="lab_bur_PositiveFairValueAdjustmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Positive Fair Value Adjustments [Member]</link:label>
    <link:label id="lab_bur_PositiveFairValueAdjustmentsMember_documentation_en-US" xlink:label="lab_bur_PositiveFairValueAdjustmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to positive fair value adjustments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_PositiveFairValueAdjustmentsMember" xlink:href="bur-20260630.xsd#bur_PositiveFairValueAdjustmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_PositiveFairValueAdjustmentsMember" xlink:to="lab_bur_PositiveFairValueAdjustmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_019e415a-4e63-7edc-ba26-81e0dd0c5735_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_019e415a-4e63-7f10-a7b5-d0594c789d94_terseLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019e415a-4e63-7b3d-b866-bc4c92283130_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_019e415a-4e64-74fe-99be-b5d0bb4d630a_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:to="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesTableTextBlock_019e415a-4dba-72f9-afb9-4904db3c70d5_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_OtherLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_OtherIncomeLoss_019e415a-4e63-7f2c-b5fe-c8b43e8040a4_verboseLabel_en-US" xlink:label="lab_bur_OtherIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other income/(loss)</link:label>
    <link:label id="lab_bur_OtherIncomeLoss_label_en-US" xlink:label="lab_bur_OtherIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income (Loss)</link:label>
    <link:label id="lab_bur_OtherIncomeLoss_documentation_en-US" xlink:label="lab_bur_OtherIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of interest and other income from capital provision assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_OtherIncomeLoss" xlink:href="bur-20260630.xsd#bur_OtherIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_OtherIncomeLoss" xlink:to="lab_bur_OtherIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_019e415a-4e64-7dc7-acc0-8f6029d510c5_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of property and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FinancialInstrumentPercentageOfIncreaseInInterestRates_019e415a-4dba-7c1c-a71f-58d52d77780f_terseLabel_en-US" xlink:label="lab_bur_FinancialInstrumentPercentageOfIncreaseInInterestRates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in interest rate (percent)</link:label>
    <link:label id="lab_bur_FinancialInstrumentPercentageOfIncreaseInInterestRates_label_en-US" xlink:label="lab_bur_FinancialInstrumentPercentageOfIncreaseInInterestRates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument, Percentage Of Increase In Interest Rates</link:label>
    <link:label id="lab_bur_FinancialInstrumentPercentageOfIncreaseInInterestRates_documentation_en-US" xlink:label="lab_bur_FinancialInstrumentPercentageOfIncreaseInInterestRates" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage of increase in interest rates.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FinancialInstrumentPercentageOfIncreaseInInterestRates" xlink:href="bur-20260630.xsd#bur_FinancialInstrumentPercentageOfIncreaseInInterestRates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FinancialInstrumentPercentageOfIncreaseInInterestRates" xlink:to="lab_bur_FinancialInstrumentPercentageOfIncreaseInInterestRates" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputExhaustionOfAllAppealsMember_019e415a-4e63-7152-b696-8d1af6e602da_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputExhaustionOfAllAppealsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exhaustion of all appeals</link:label>
    <link:label id="lab_bur_MeasurementInputExhaustionOfAllAppealsMember_label_en-US" xlink:label="lab_bur_MeasurementInputExhaustionOfAllAppealsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Exhaustion Of All Appeals [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputExhaustionOfAllAppealsMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputExhaustionOfAllAppealsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using Exhaustion of all appeals.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputExhaustionOfAllAppealsMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputExhaustionOfAllAppealsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputExhaustionOfAllAppealsMember" xlink:to="lab_bur_MeasurementInputExhaustionOfAllAppealsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_TransferOfRealizationsFromDerivativeAssets_019e415a-4e64-7257-b96c-cd1e40d3f8e2_terseLabel_en-US" xlink:label="lab_bur_TransferOfRealizationsFromDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer of realizations from capital provision assets</link:label>
    <link:label id="lab_bur_TransferOfRealizationsFromDerivativeAssets_label_en-US" xlink:label="lab_bur_TransferOfRealizationsFromDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfer Of Realizations From Derivative Assets</link:label>
    <link:label id="lab_bur_TransferOfRealizationsFromDerivativeAssets_documentation_en-US" xlink:label="lab_bur_TransferOfRealizationsFromDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transfer of realizations from capital provision assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_TransferOfRealizationsFromDerivativeAssets" xlink:href="bur-20260630.xsd#bur_TransferOfRealizationsFromDerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_TransferOfRealizationsFromDerivativeAssets" xlink:to="lab_bur_TransferOfRealizationsFromDerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_SingleCasePortfolioJointVenturesAndEquityMethodInvestmentsLegalRiskManagementCoreLegalFinanceFinancialLiabilitiesRelatingToThirdPartyInterestsInCapitalProvisionAssetsMember_019e415a-4dba-737f-8997-d7a248d6c58b_terseLabel_en-US" xlink:label="lab_bur_SingleCasePortfolioJointVenturesAndEquityMethodInvestmentsLegalRiskManagementCoreLegalFinanceFinancialLiabilitiesRelatingToThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Single case, Portfolio, Joint ventures and equity method investments, Legal risk management, Core legal finance (BOF-C)(1), Core legal finance (EP Funds), Financial liabilities relating to third party interests in capital provision assets</link:label>
    <link:label id="lab_bur_SingleCasePortfolioJointVenturesAndEquityMethodInvestmentsLegalRiskManagementCoreLegalFinanceFinancialLiabilitiesRelatingToThirdPartyInterestsInCapitalProvisionAssetsMember_label_en-US" xlink:label="lab_bur_SingleCasePortfolioJointVenturesAndEquityMethodInvestmentsLegalRiskManagementCoreLegalFinanceFinancialLiabilitiesRelatingToThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Single Case, Portfolio, Joint Ventures And Equity Method Investments, Legal Risk Management, Core Legal Finance, Financial Liabilities Relating To Third Party Interests In Capital Provision Assets [Member]</link:label>
    <link:label id="lab_bur_SingleCasePortfolioJointVenturesAndEquityMethodInvestmentsLegalRiskManagementCoreLegalFinanceFinancialLiabilitiesRelatingToThirdPartyInterestsInCapitalProvisionAssetsMember_documentation_en-US" xlink:label="lab_bur_SingleCasePortfolioJointVenturesAndEquityMethodInvestmentsLegalRiskManagementCoreLegalFinanceFinancialLiabilitiesRelatingToThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Single Case, Portfolio, Joint Ventures And Equity Method Investments, Legal Risk Management, Core Legal Finance, Financial Liabilities Relating To Third Party Interests In Capital Provision Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_SingleCasePortfolioJointVenturesAndEquityMethodInvestmentsLegalRiskManagementCoreLegalFinanceFinancialLiabilitiesRelatingToThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:href="bur-20260630.xsd#bur_SingleCasePortfolioJointVenturesAndEquityMethodInvestmentsLegalRiskManagementCoreLegalFinanceFinancialLiabilitiesRelatingToThirdPartyInterestsInCapitalProvisionAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_SingleCasePortfolioJointVenturesAndEquityMethodInvestmentsLegalRiskManagementCoreLegalFinanceFinancialLiabilitiesRelatingToThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:to="lab_bur_SingleCasePortfolioJointVenturesAndEquityMethodInvestmentsLegalRiskManagementCoreLegalFinanceFinancialLiabilitiesRelatingToThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccountsReceivableUnrealizedGainLoss_019e415a-4dba-7d9c-afc5-8ceabec99fc0_terseLabel_en-US" xlink:label="lab_bur_AccountsReceivableUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from settlement of capital provision assets, Unrealized</link:label>
    <link:label id="lab_bur_AccountsReceivableUnrealizedGainLoss_label_en-US" xlink:label="lab_bur_AccountsReceivableUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_bur_AccountsReceivableUnrealizedGainLoss_documentation_en-US" xlink:label="lab_bur_AccountsReceivableUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccountsReceivableUnrealizedGainLoss" xlink:href="bur-20260630.xsd#bur_AccountsReceivableUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccountsReceivableUnrealizedGainLoss" xlink:to="lab_bur_AccountsReceivableUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsPurchases_019e415a-4e63-7b6b-90b6-bd96491bb32a_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deployments</link:label>
    <link:label id="lab_bur_DerivativeAssetsPurchases_label_en-US" xlink:label="lab_bur_DerivativeAssetsPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets, Purchases</link:label>
    <link:label id="lab_bur_DerivativeAssetsPurchases_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsPurchases" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital provision assets deployments during the period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsPurchases" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsPurchases" xlink:to="lab_bur_DerivativeAssetsPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_019e415a-4dba-76e9-9cad-94e9edc947af_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit risk from financial instruments</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskLineItems" xlink:to="lab_us-gaap_ConcentrationRiskLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019e415a-4dba-7a23-9ec8-6f672a3ff0ac_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding as of</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_CashAndCashEquivalentsAndMarketableSecurities_019e415a-4dba-73f8-800d-d2ca3ab3e2ad_terseLabel_en-US" xlink:label="lab_bur_CashAndCashEquivalentsAndMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents and marketable securities</link:label>
    <link:label id="lab_bur_CashAndCashEquivalentsAndMarketableSecurities_label_en-US" xlink:label="lab_bur_CashAndCashEquivalentsAndMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash And Cash Equivalents And Marketable Securities</link:label>
    <link:label id="lab_bur_CashAndCashEquivalentsAndMarketableSecurities_documentation_en-US" xlink:label="lab_bur_CashAndCashEquivalentsAndMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash And Cash Equivalents And Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_CashAndCashEquivalentsAndMarketableSecurities" xlink:href="bur-20260630.xsd#bur_CashAndCashEquivalentsAndMarketableSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_CashAndCashEquivalentsAndMarketableSecurities" xlink:to="lab_bur_CashAndCashEquivalentsAndMarketableSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearTwo_019e415a-4dba-7451-b4fd-46bce33de003_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearTwo_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments of Principal in Rolling Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearTwo" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019e415a-4dba-7fc6-a5e2-566da498a383_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_IndenturesGoverning2028Notes2030NotesAnd2031NotesMember_019e415a-4dba-7ed1-ae65-ffd7df41761e_terseLabel_en-US" xlink:label="lab_bur_IndenturesGoverning2028Notes2030NotesAnd2031NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indentures governing the 2028 Notes, the 2030 Notes and the 2031 Notes</link:label>
    <link:label id="lab_bur_IndenturesGoverning2028Notes2030NotesAnd2031NotesMember_label_en-US" xlink:label="lab_bur_IndenturesGoverning2028Notes2030NotesAnd2031NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indentures Governing 2028 Notes, 2030 Notes And 2031 Notes [Member]</link:label>
    <link:label id="lab_bur_IndenturesGoverning2028Notes2030NotesAnd2031NotesMember_documentation_en-US" xlink:label="lab_bur_IndenturesGoverning2028Notes2030NotesAnd2031NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to indentures governing the 2028 Notes, the 2030 Notes and the 2031 Notes.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_IndenturesGoverning2028Notes2030NotesAnd2031NotesMember" xlink:href="bur-20260630.xsd#bur_IndenturesGoverning2028Notes2030NotesAnd2031NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_IndenturesGoverning2028Notes2030NotesAnd2031NotesMember" xlink:to="lab_bur_IndenturesGoverning2028Notes2030NotesAnd2031NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e415a-4e63-742b-9b22-69c911a38bdc_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e415a-4e63-7a93-a5bc-562756a49955_totalLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_019e415a-4e64-7350-beee-aa406eff2163_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset management income</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:to="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019e415a-4e63-71aa-8afa-572ad167430a_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_019e415a-4dba-7c1f-9920-b01bf795aed4_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditLossAbstract_label_en-US" xlink:label="lab_us-gaap_CreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditLossAbstract" xlink:to="lab_us-gaap_CreditLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_019e415a-4e63-77b4-a4ab-c537b4bf5f85_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital provision assets</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputAdjustedRiskPremiumMember_019e415a-4e63-798f-aaa3-45aea67c47fa_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputAdjustedRiskPremiumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjusted risk premium</link:label>
    <link:label id="lab_bur_MeasurementInputAdjustedRiskPremiumMember_label_en-US" xlink:label="lab_bur_MeasurementInputAdjustedRiskPremiumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Adjusted Risk Premium [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputAdjustedRiskPremiumMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputAdjustedRiskPremiumMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using adjusted risk premium.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputAdjustedRiskPremiumMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputAdjustedRiskPremiumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputAdjustedRiskPremiumMember" xlink:to="lab_bur_MeasurementInputAdjustedRiskPremiumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_019e415a-4dba-721f-ab33-755fc76202e9_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_019e415a-4dba-71f7-8978-8f318637025a_totalLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Maximum exposure to loss</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:to="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ChangeInExpectedTimingDomain_019e415a-4e63-761a-8e46-f641e44b1c79_terseLabel_en-US" xlink:label="lab_bur_ChangeInExpectedTimingDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change In Expected Timing [Domain]</link:label>
    <link:label id="lab_bur_ChangeInExpectedTimingDomain_label_en-US" xlink:label="lab_bur_ChangeInExpectedTimingDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change In Expected Timing [Domain]</link:label>
    <link:label id="lab_bur_ChangeInExpectedTimingDomain_documentation_en-US" xlink:label="lab_bur_ChangeInExpectedTimingDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Change In Expected Timing [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ChangeInExpectedTimingDomain" xlink:href="bur-20260630.xsd#bur_ChangeInExpectedTimingDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ChangeInExpectedTimingDomain" xlink:to="lab_bur_ChangeInExpectedTimingDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_CapitalProvisionAssetsSingleWithEquityRiskMember_019e415a-4e63-758d-9ff1-8af8c052a69e_terseLabel_en-US" xlink:label="lab_bur_CapitalProvisionAssetsSingleWithEquityRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Single case with equity risk</link:label>
    <link:label id="lab_bur_CapitalProvisionAssetsSingleWithEquityRiskMember_label_en-US" xlink:label="lab_bur_CapitalProvisionAssetsSingleWithEquityRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Provision Assets Single With Equity Risk [Member]</link:label>
    <link:label id="lab_bur_CapitalProvisionAssetsSingleWithEquityRiskMember_documentation_en-US" xlink:label="lab_bur_CapitalProvisionAssetsSingleWithEquityRiskMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents information relating to capital provision assets single with equity risk.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_CapitalProvisionAssetsSingleWithEquityRiskMember" xlink:href="bur-20260630.xsd#bur_CapitalProvisionAssetsSingleWithEquityRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_CapitalProvisionAssetsSingleWithEquityRiskMember" xlink:to="lab_bur_CapitalProvisionAssetsSingleWithEquityRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019e415a-4dba-75a6-b9d5-247de6328471_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Analysis of the Movements in the Level 3 Financial Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ScheduleOfUnamortizedIssuanceCostsAndTotalFinanceCostsTableTextBlock_019e415a-4e63-787c-9fbd-d5c70d51d089_terseLabel_en-US" xlink:label="lab_bur_ScheduleOfUnamortizedIssuanceCostsAndTotalFinanceCostsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Unamortized Issuance Costs and Total Finance Costs</link:label>
    <link:label id="lab_bur_ScheduleOfUnamortizedIssuanceCostsAndTotalFinanceCostsTableTextBlock_label_en-US" xlink:label="lab_bur_ScheduleOfUnamortizedIssuanceCostsAndTotalFinanceCostsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Unamortized Issuance Costs And Total Finance Costs [Table Text Block]</link:label>
    <link:label id="lab_bur_ScheduleOfUnamortizedIssuanceCostsAndTotalFinanceCostsTableTextBlock_documentation_en-US" xlink:label="lab_bur_ScheduleOfUnamortizedIssuanceCostsAndTotalFinanceCostsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tabular disclosure of changes from cash flows and non-cash changes of debt issued.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ScheduleOfUnamortizedIssuanceCostsAndTotalFinanceCostsTableTextBlock" xlink:href="bur-20260630.xsd#bur_ScheduleOfUnamortizedIssuanceCostsAndTotalFinanceCostsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ScheduleOfUnamortizedIssuanceCostsAndTotalFinanceCostsTableTextBlock" xlink:to="lab_bur_ScheduleOfUnamortizedIssuanceCostsAndTotalFinanceCostsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_PerformanceFeeIncomeMember_019e415a-4dba-7683-b5db-6a3330ccc014_terseLabel_en-US" xlink:label="lab_bur_PerformanceFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance fee income</link:label>
    <link:label id="lab_bur_PerformanceFeeIncomeMember_label_en-US" xlink:label="lab_bur_PerformanceFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Fee Income [Member]</link:label>
    <link:label id="lab_bur_PerformanceFeeIncomeMember_documentation_en-US" xlink:label="lab_bur_PerformanceFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents information pertaining to performance fees.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_PerformanceFeeIncomeMember" xlink:href="bur-20260630.xsd#bur_PerformanceFeeIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_PerformanceFeeIncomeMember" xlink:to="lab_bur_PerformanceFeeIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_019e415a-4e63-70f9-803e-1a86fb91501f_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury shares</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonMember" xlink:to="lab_us-gaap_TreasuryStockCommonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_019e415a-4e63-7e44-9c9f-7d144f209ca9_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based and deferred compensation</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019e415a-4dba-7f95-ba81-ec081fdae429_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableFairValueDisclosure_019e415a-4e63-7261-8398-4f320796f02b_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from settlement of capital provision assets</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableFairValueDisclosure" xlink:to="lab_us-gaap_AccountsReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_019e415a-4dba-76a7-b0ed-5b3b8bccf1bb_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective tax rates</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_019e415a-4dba-71ef-8aa5-78483d8dc4ee_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of financial instruments</link:label>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_label_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_PercentageOfDiscreteObjectiveLitigationEvents_019e415a-4dba-749b-9b6a-3374888404dc_terseLabel_en-US" xlink:label="lab_bur_PercentageOfDiscreteObjectiveLitigationEvents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of discrete objective litigation events</link:label>
    <link:label id="lab_bur_PercentageOfDiscreteObjectiveLitigationEvents_label_en-US" xlink:label="lab_bur_PercentageOfDiscreteObjectiveLitigationEvents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Of Discrete Objective Litigation Events</link:label>
    <link:label id="lab_bur_PercentageOfDiscreteObjectiveLitigationEvents_documentation_en-US" xlink:label="lab_bur_PercentageOfDiscreteObjectiveLitigationEvents" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The percentage of discrete objective litigation events.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_PercentageOfDiscreteObjectiveLitigationEvents" xlink:href="bur-20260630.xsd#bur_PercentageOfDiscreteObjectiveLitigationEvents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_PercentageOfDiscreteObjectiveLitigationEvents" xlink:to="lab_bur_PercentageOfDiscreteObjectiveLitigationEvents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_019e415a-4e63-705b-8ba3-37fbb6def6fd_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dilutive effect of share-based awards (in shares)</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Share-Based Payment Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:to="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_PaymentsForFundingOfDerivativeAssets_019e415a-4e64-7d36-a13c-a89fd0cb9366_negatedLabel_en-US" xlink:label="lab_bur_PaymentsForFundingOfDerivativeAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Deployments to capital provision assets</link:label>
    <link:label id="lab_bur_PaymentsForFundingOfDerivativeAssets_label_en-US" xlink:label="lab_bur_PaymentsForFundingOfDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For Funding Of Derivative Assets</link:label>
    <link:label id="lab_bur_PaymentsForFundingOfDerivativeAssets_documentation_en-US" xlink:label="lab_bur_PaymentsForFundingOfDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The cash outflow from funding of capital provision asset.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_PaymentsForFundingOfDerivativeAssets" xlink:href="bur-20260630.xsd#bur_PaymentsForFundingOfDerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_PaymentsForFundingOfDerivativeAssets" xlink:to="lab_bur_PaymentsForFundingOfDerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_019e415a-4e64-7f3c-a39e-56ec11d2db9a_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_A5.0DueDec2026Member_019e415a-4dba-735d-b1e8-fd8eee047a05_terseLabel_en-US" xlink:label="lab_bur_A5.0DueDec2026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.000% Bonds due 2026</link:label>
    <link:label id="lab_bur_A5.0DueDec2026Member_label_en-US" xlink:label="lab_bur_A5.0DueDec2026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5.0% Due Dec 2026 [Member]</link:label>
    <link:label id="lab_bur_A5.0DueDec2026Member_documentation_en-US" xlink:label="lab_bur_A5.0DueDec2026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining Bonds issued at 6.125 percent due December 2026.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_A5.0DueDec2026Member" xlink:href="bur-20260630.xsd#bur_A5.0DueDec2026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_A5.0DueDec2026Member" xlink:to="lab_bur_A5.0DueDec2026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_VariableInterestEntityOnBalanceSheetExposure_019e415a-4e63-760b-a9c2-3c0b22bf8b81_terseLabel_en-US" xlink:label="lab_bur_VariableInterestEntityOnBalanceSheetExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">On-balance sheet exposure</link:label>
    <link:label id="lab_bur_VariableInterestEntityOnBalanceSheetExposure_label_en-US" xlink:label="lab_bur_VariableInterestEntityOnBalanceSheetExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, On Balance Sheet Exposure</link:label>
    <link:label id="lab_bur_VariableInterestEntityOnBalanceSheetExposure_documentation_en-US" xlink:label="lab_bur_VariableInterestEntityOnBalanceSheetExposure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The amount of on balance sheet exposure.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_VariableInterestEntityOnBalanceSheetExposure" xlink:href="bur-20260630.xsd#bur_VariableInterestEntityOnBalanceSheetExposure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_VariableInterestEntityOnBalanceSheetExposure" xlink:to="lab_bur_VariableInterestEntityOnBalanceSheetExposure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_019e415a-4dba-724d-bf71-3022e1b11956_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputOtherMember_019e415a-4e63-7e50-9cca-94c7f1d06440_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_bur_MeasurementInputOtherMember_label_en-US" xlink:label="lab_bur_MeasurementInputOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Other [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputOtherMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputOtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input related to other.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputOtherMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputOtherMember" xlink:to="lab_bur_MeasurementInputOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextRollingTwelveMonths_019e415a-4e63-7ed0-a91d-bc2e54bcbb17_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextRollingTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextRollingTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextRollingTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments of Principal in Next Rolling 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextRollingTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextRollingTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextRollingTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextRollingTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesDisclosureTextBlock_019e415a-4e63-72cc-9750-c65448922037_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesDisclosureTextBlock" xlink:to="lab_us-gaap_OtherLiabilitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_019e415a-4dba-71f2-9e07-bbaf0223170d_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:to="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsThirdPartyInterestsMember_019e415a-4dba-7ab9-ba7a-25b1df6f227c_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsThirdPartyInterestsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Core legal finance (EP Funds), third party interests</link:label>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsThirdPartyInterestsMember_label_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsThirdPartyInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets Core Legal Finance EP Funds, Third Party Interests [Member]</link:label>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsThirdPartyInterestsMember_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsThirdPartyInterestsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Assets Core Legal Finance EP Funds, Third Party Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsCoreLegalFinanceEPFundsThirdPartyInterestsMember" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsCoreLegalFinanceEPFundsThirdPartyInterestsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsCoreLegalFinanceEPFundsThirdPartyInterestsMember" xlink:to="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsThirdPartyInterestsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019e415a-4e63-7935-81ef-e5dc0282ea75_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Computation for Basic and Diluted Net Income Per Ordinary Share</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019e415a-4e63-7628-82ff-aaa6cabc1bb1_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_019e415a-4e63-77cb-ad94-5dc53e4c28a8_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment reporting</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCredit_019e415a-4e63-7456-853f-04d5cdcb8864_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit</link:label>
    <link:label id="lab_us-gaap_LineOfCredit_label_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCredit" xlink:to="lab_us-gaap_LineOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_019e415a-4dba-72d6-a953-59bde73a35cd_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_019e415a-4e64-75f9-8b74-49f58ac30a8e_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase/(decrease) in cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Excluding Exchange Rate Effect, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputTrialCourtJudgmentOrTribunalAwardMember_019e415a-4dba-7a77-b8de-dde94583c06e_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputTrialCourtJudgmentOrTribunalAwardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trial court judgment or tribunal award</link:label>
    <link:label id="lab_bur_MeasurementInputTrialCourtJudgmentOrTribunalAwardMember_label_en-US" xlink:label="lab_bur_MeasurementInputTrialCourtJudgmentOrTribunalAwardMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Trial Court Judgment Or Tribunal Award [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputTrialCourtJudgmentOrTribunalAwardMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputTrialCourtJudgmentOrTribunalAwardMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using trial court judgment or tribunal award.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputTrialCourtJudgmentOrTribunalAwardMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputTrialCourtJudgmentOrTribunalAwardMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputTrialCourtJudgmentOrTribunalAwardMember" xlink:to="lab_bur_MeasurementInputTrialCourtJudgmentOrTribunalAwardMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_019e415a-4dba-7524-99d6-94863df82a90_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedProfessionalFeesCurrentAndNoncurrent_019e415a-4dba-7bb9-9c01-308b1f7ac99f_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedProfessionalFeesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Audit fees payable</link:label>
    <link:label id="lab_us-gaap_AccruedProfessionalFeesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccruedProfessionalFeesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Professional Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedProfessionalFeesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedProfessionalFeesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedProfessionalFeesCurrentAndNoncurrent" xlink:to="lab_us-gaap_AccruedProfessionalFeesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_019e415a-4dba-78df-ab4e-8aac56b3a0cc_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Asset Management Income</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:to="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityDisclosureTextBlock_019e415a-4e63-7cdf-abdf-c61a35e8ffac_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable interest entities</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:to="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_019e415a-4dba-7e42-bb49-d1de96b181d5_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_A6MonthsDurationMember_019e415a-4e63-7072-bbab-9e8501b08782_terseLabel_en-US" xlink:label="lab_bur_A6MonthsDurationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">6 months duration</link:label>
    <link:label id="lab_bur_A6MonthsDurationMember_label_en-US" xlink:label="lab_bur_A6MonthsDurationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">6 Months Duration [Member]</link:label>
    <link:label id="lab_bur_A6MonthsDurationMember_documentation_en-US" xlink:label="lab_bur_A6MonthsDurationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the member information pertaining to expected timing of a favorable outcome of six months.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_A6MonthsDurationMember" xlink:href="bur-20260630.xsd#bur_A6MonthsDurationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_A6MonthsDurationMember" xlink:to="lab_bur_A6MonthsDurationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e415a-4e63-74e9-98f3-58bc95e5dcdc_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of exchange rate changes on cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_019e415a-4dba-76f2-b451-d2c188f24406_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets, Goodwill, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e415a-4e63-7a9b-81ee-3a3000d8a741_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total shareholders' equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e415a-4e63-7f49-8a54-94a40cc29852_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at the beginning</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e415a-4e63-7515-b718-08b22027a67a_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at the end</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_WeightedAverageSharesOutstandingAbstract_019e415a-4e63-729f-8ef6-f04a16fb28a5_terseLabel_en-US" xlink:label="lab_bur_WeightedAverageSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average ordinary shares outstanding</link:label>
    <link:label id="lab_bur_WeightedAverageSharesOutstandingAbstract_label_en-US" xlink:label="lab_bur_WeightedAverageSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted-Average Shares Outstanding [Abstract]</link:label>
    <link:label id="lab_bur_WeightedAverageSharesOutstandingAbstract_documentation_en-US" xlink:label="lab_bur_WeightedAverageSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">No definition available.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_WeightedAverageSharesOutstandingAbstract" xlink:href="bur-20260630.xsd#bur_WeightedAverageSharesOutstandingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_WeightedAverageSharesOutstandingAbstract" xlink:to="lab_bur_WeightedAverageSharesOutstandingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetMeasurementInput_019e415a-4e64-7d38-84e1-bfcd5060441f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital provision assets, measurement input</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetMeasurementInput" xlink:to="lab_us-gaap_DerivativeAssetMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsPortfolioWithEquityRiskAndCoreLegalFinanceMember_019e415a-4dba-7292-b116-78909b6de199_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsPortfolioWithEquityRiskAndCoreLegalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portfolio with equity risk, Core legal finance (BOF-C)</link:label>
    <link:label id="lab_bur_DerivativeAssetsPortfolioWithEquityRiskAndCoreLegalFinanceMember_label_en-US" xlink:label="lab_bur_DerivativeAssetsPortfolioWithEquityRiskAndCoreLegalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets, Portfolio With Equity Risk And Core Legal Finance [Member]</link:label>
    <link:label id="lab_bur_DerivativeAssetsPortfolioWithEquityRiskAndCoreLegalFinanceMember_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsPortfolioWithEquityRiskAndCoreLegalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Assets, Portfolio With Equity Risk And Core Legal Finance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsPortfolioWithEquityRiskAndCoreLegalFinanceMember" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsPortfolioWithEquityRiskAndCoreLegalFinanceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsPortfolioWithEquityRiskAndCoreLegalFinanceMember" xlink:to="lab_bur_DerivativeAssetsPortfolioWithEquityRiskAndCoreLegalFinanceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilities_019e415a-4dba-7dee-b0ed-0e1969a411ca_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_019e415a-4dba-74ce-89da-2c4af15d8518_totalLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStock_019e415a-4e64-7d93-a18e-3b892743cc84_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStock" xlink:to="lab_us-gaap_DividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AssetsLiabilitiesNetUnrealizedGainLoss_019e415a-4dba-714c-b115-5557efb33598_terseLabel_en-US" xlink:label="lab_bur_AssetsLiabilitiesNetUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset (Liability) unrealized</link:label>
    <link:label id="lab_bur_AssetsLiabilitiesNetUnrealizedGainLoss_label_en-US" xlink:label="lab_bur_AssetsLiabilitiesNetUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets (Liabilities) Net, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_bur_AssetsLiabilitiesNetUnrealizedGainLoss_documentation_en-US" xlink:label="lab_bur_AssetsLiabilitiesNetUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of unrealized gain (loss) on net assets (liabilities).</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AssetsLiabilitiesNetUnrealizedGainLoss" xlink:href="bur-20260630.xsd#bur_AssetsLiabilitiesNetUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AssetsLiabilitiesNetUnrealizedGainLoss" xlink:to="lab_bur_AssetsLiabilitiesNetUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock_019e415a-4dba-75ab-b34f-b9857861bfd8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Carrying Values and Estimated Fair Values of Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FinancialInstrumentPercentageOfDecreaseInInterestRates_019e415a-4dba-75a5-8436-fc2c43e12fc8_terseLabel_en-US" xlink:label="lab_bur_FinancialInstrumentPercentageOfDecreaseInInterestRates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Decrease in interest rate (percent)</link:label>
    <link:label id="lab_bur_FinancialInstrumentPercentageOfDecreaseInInterestRates_label_en-US" xlink:label="lab_bur_FinancialInstrumentPercentageOfDecreaseInInterestRates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument, Percentage Of Decrease In Interest Rates</link:label>
    <link:label id="lab_bur_FinancialInstrumentPercentageOfDecreaseInInterestRates_documentation_en-US" xlink:label="lab_bur_FinancialInstrumentPercentageOfDecreaseInInterestRates" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage of decrease in interest rates.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FinancialInstrumentPercentageOfDecreaseInInterestRates" xlink:href="bur-20260630.xsd#bur_FinancialInstrumentPercentageOfDecreaseInInterestRates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FinancialInstrumentPercentageOfDecreaseInInterestRates" xlink:to="lab_bur_FinancialInstrumentPercentageOfDecreaseInInterestRates" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetForeignExchangeGainLoss_019e415a-4dba-7c2f-96fc-7c617a920da9_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetForeignExchangeGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange gains/(losses)</link:label>
    <link:label id="lab_bur_DerivativeAssetForeignExchangeGainLoss_label_en-US" xlink:label="lab_bur_DerivativeAssetForeignExchangeGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Foreign Exchange Gain (Loss)</link:label>
    <link:label id="lab_bur_DerivativeAssetForeignExchangeGainLoss_documentation_en-US" xlink:label="lab_bur_DerivativeAssetForeignExchangeGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital provision assets foreign exchange gains or losses during the period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetForeignExchangeGainLoss" xlink:href="bur-20260630.xsd#bur_DerivativeAssetForeignExchangeGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetForeignExchangeGainLoss" xlink:to="lab_bur_DerivativeAssetForeignExchangeGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_019e415a-4dba-7ca9-93ba-0d451119820c_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_019e415a-4dba-78e3-9412-4592cc3a77c8_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment reporting</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_019e415a-4dba-775e-95d3-b438f489921c_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_019e415a-4dba-77cf-a3ce-1e89dd62c1c9_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_019e415a-4e63-740d-a54d-46ec2a9fca8c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_019e415a-4e63-72e6-b0e6-eb301f706c7e_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_019e415a-4e63-71c3-bdc7-66a0c1261508_verboseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unamortized issuance costs</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecuritiesGainLossExcludingOtherThanTemporaryImpairments_019e415a-4dba-7a6d-8c6c-f8730c6c605c_negatedLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesGainLossExcludingOtherThanTemporaryImpairments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">(Income)/loss on marketable securities</link:label>
    <link:label id="lab_us-gaap_MarketableSecuritiesGainLossExcludingOtherThanTemporaryImpairments_label_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesGainLossExcludingOtherThanTemporaryImpairments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Security, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecuritiesGainLossExcludingOtherThanTemporaryImpairments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MarketableSecuritiesGainLossExcludingOtherThanTemporaryImpairments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecuritiesGainLossExcludingOtherThanTemporaryImpairments" xlink:to="lab_us-gaap_MarketableSecuritiesGainLossExcludingOtherThanTemporaryImpairments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_019e415a-4dba-7326-ae4e-959b2c94a733_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_019e415a-4dba-72e7-b230-954e7c30e2d5_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_019e415a-4e63-7ccc-a2d4-e81324999d76_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) for the period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccruedBonusesChangeFromForeignExchangeGainLosses_019e415a-4dba-7ccb-9493-07247bdfe0c0_terseLabel_en-US" xlink:label="lab_bur_AccruedBonusesChangeFromForeignExchangeGainLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange gains/(losses)</link:label>
    <link:label id="lab_bur_AccruedBonusesChangeFromForeignExchangeGainLosses_label_en-US" xlink:label="lab_bur_AccruedBonusesChangeFromForeignExchangeGainLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Bonuses, Change From Foreign Exchange Gain (Losses)</link:label>
    <link:label id="lab_bur_AccruedBonusesChangeFromForeignExchangeGainLosses_documentation_en-US" xlink:label="lab_bur_AccruedBonusesChangeFromForeignExchangeGainLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of change in long term incentive compensation payable by foreign exchange gain (losses).</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccruedBonusesChangeFromForeignExchangeGainLosses" xlink:href="bur-20260630.xsd#bur_AccruedBonusesChangeFromForeignExchangeGainLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccruedBonusesChangeFromForeignExchangeGainLosses" xlink:to="lab_bur_AccruedBonusesChangeFromForeignExchangeGainLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments_019e415a-4dba-7435-ae52-196fe48fc0fe_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Acquisitions of equity method and other investments</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019e415a-4e64-7866-8270-7027e7f51212_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019e415a-4dba-7bdf-8124-9fe693a97003_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Burford Capital Limited equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DebtInstrumentCovenantMinimumPrincipalAmountGuaranteedToBeRequiredToGuaranteeNotes_019e415a-4dba-75bf-9359-ee52141161a6_terseLabel_en-US" xlink:label="lab_bur_DebtInstrumentCovenantMinimumPrincipalAmountGuaranteedToBeRequiredToGuaranteeNotes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum principal amount</link:label>
    <link:label id="lab_bur_DebtInstrumentCovenantMinimumPrincipalAmountGuaranteedToBeRequiredToGuaranteeNotes_label_en-US" xlink:label="lab_bur_DebtInstrumentCovenantMinimumPrincipalAmountGuaranteedToBeRequiredToGuaranteeNotes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant, Minimum Principal Amount Guaranteed To Be Required To Guarantee Notes</link:label>
    <link:label id="lab_bur_DebtInstrumentCovenantMinimumPrincipalAmountGuaranteedToBeRequiredToGuaranteeNotes_documentation_en-US" xlink:label="lab_bur_DebtInstrumentCovenantMinimumPrincipalAmountGuaranteedToBeRequiredToGuaranteeNotes" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant, Minimum Principal Amount Guaranteed To Be Required To Guarantee Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DebtInstrumentCovenantMinimumPrincipalAmountGuaranteedToBeRequiredToGuaranteeNotes" xlink:href="bur-20260630.xsd#bur_DebtInstrumentCovenantMinimumPrincipalAmountGuaranteedToBeRequiredToGuaranteeNotes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DebtInstrumentCovenantMinimumPrincipalAmountGuaranteedToBeRequiredToGuaranteeNotes" xlink:to="lab_bur_DebtInstrumentCovenantMinimumPrincipalAmountGuaranteedToBeRequiredToGuaranteeNotes" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromInterestAndDividendsReceived_019e415a-4e63-7041-91cf-d1113eecc772_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromInterestAndDividendsReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash received from interest and dividend income</link:label>
    <link:label id="lab_us-gaap_ProceedsFromInterestAndDividendsReceived_label_en-US" xlink:label="lab_us-gaap_ProceedsFromInterestAndDividendsReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Interest and Dividends Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromInterestAndDividendsReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromInterestAndDividendsReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromInterestAndDividendsReceived" xlink:to="lab_us-gaap_ProceedsFromInterestAndDividendsReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_019e415a-4e63-7f13-b763-dced5ff5dedb_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total other expenses</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpense" xlink:to="lab_us-gaap_NonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_UnsecuredNotes7.500PercentDueJuly2033Member_019e415a-4e63-7095-8eeb-e139f5bd77da_terseLabel_en-US" xlink:label="lab_bur_UnsecuredNotes7.500PercentDueJuly2033Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">7.500% Senior Notes due July 15, 2033</link:label>
    <link:label id="lab_bur_UnsecuredNotes7.500PercentDueJuly2033Member_label_en-US" xlink:label="lab_bur_UnsecuredNotes7.500PercentDueJuly2033Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Notes 7.500 Percent Due July 2033 [Member]</link:label>
    <link:label id="lab_bur_UnsecuredNotes7.500PercentDueJuly2033Member_documentation_en-US" xlink:label="lab_bur_UnsecuredNotes7.500PercentDueJuly2033Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Notes 7.500 Percent Due July 2033</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_UnsecuredNotes7.500PercentDueJuly2033Member" xlink:href="bur-20260630.xsd#bur_UnsecuredNotes7.500PercentDueJuly2033Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_UnsecuredNotes7.500PercentDueJuly2033Member" xlink:to="lab_bur_UnsecuredNotes7.500PercentDueJuly2033Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019e415a-4dba-76fe-9c8d-1f718f3de819_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:to="lab_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfCapitalDistribution_019e415a-4e63-7c71-b23a-cebfdee17ada_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfCapitalDistribution" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Third-party net capital contribution/(distribution)</link:label>
    <link:label id="lab_us-gaap_PaymentsOfCapitalDistribution_label_en-US" xlink:label="lab_us-gaap_PaymentsOfCapitalDistribution" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Capital Distribution</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfCapitalDistribution" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfCapitalDistribution"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfCapitalDistribution" xlink:to="lab_us-gaap_PaymentsOfCapitalDistribution" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019e415a-4dba-7302-9295-2d1f87fabd04_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DebtInstrumentRedemptionPriceProceedsNotAppliedAsPermittedPercentage_019e415a-4dba-750e-ac30-cc4da4e44b64_terseLabel_en-US" xlink:label="lab_bur_DebtInstrumentRedemptionPriceProceedsNotAppliedAsPermittedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption price, proceeds not applied as permitted, percentage</link:label>
    <link:label id="lab_bur_DebtInstrumentRedemptionPriceProceedsNotAppliedAsPermittedPercentage_label_en-US" xlink:label="lab_bur_DebtInstrumentRedemptionPriceProceedsNotAppliedAsPermittedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Proceeds Not Applied As Permitted, Percentage</link:label>
    <link:label id="lab_bur_DebtInstrumentRedemptionPriceProceedsNotAppliedAsPermittedPercentage_documentation_en-US" xlink:label="lab_bur_DebtInstrumentRedemptionPriceProceedsNotAppliedAsPermittedPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Proceeds Not Applied As Permitted, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DebtInstrumentRedemptionPriceProceedsNotAppliedAsPermittedPercentage" xlink:href="bur-20260630.xsd#bur_DebtInstrumentRedemptionPriceProceedsNotAppliedAsPermittedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DebtInstrumentRedemptionPriceProceedsNotAppliedAsPermittedPercentage" xlink:to="lab_bur_DebtInstrumentRedemptionPriceProceedsNotAppliedAsPermittedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIncomeTaxRefunds_019e415a-4dba-7565-9d67-eedb90064eeb_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIncomeTaxRefunds" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash received from income tax refund</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIncomeTaxRefunds_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIncomeTaxRefunds" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Income Tax Refunds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIncomeTaxRefunds" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIncomeTaxRefunds"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIncomeTaxRefunds" xlink:to="lab_us-gaap_ProceedsFromIncomeTaxRefunds" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased_019e415a-4e63-7b54-b3dd-b17a1ae90e1d_terseLabel_en-US" xlink:label="lab_srt_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Authorized repurchase amount (in shares)</link:label>
    <link:label id="lab_srt_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased_label_en-US" xlink:label="lab_srt_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Authorized, Number of Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased" xlink:to="lab_srt_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019e415a-4e63-7691-88ec-a9693424c0c0_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_019e415a-4e63-7f46-9322-df88788e9cd4_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax (benefit)/expense</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesFairValueDisclosure_019e415a-4dba-7b50-8256-fc98b7b2c120_terseLabel_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets of consolidated investment companies</link:label>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesFairValueDisclosure_label_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Of Consolidated Investment Companies, Fair Value Disclosure</link:label>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesFairValueDisclosure_documentation_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets Of Consolidated Investment Companies, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AssetsOfConsolidatedInvestmentCompaniesFairValueDisclosure" xlink:href="bur-20260630.xsd#bur_AssetsOfConsolidatedInvestmentCompaniesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AssetsOfConsolidatedInvestmentCompaniesFairValueDisclosure" xlink:to="lab_bur_AssetsOfConsolidatedInvestmentCompaniesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ScheduleOfAccruedBonusesTableTextBlock_019e415a-4dba-751c-ac69-3f83651796bd_terseLabel_en-US" xlink:label="lab_bur_ScheduleOfAccruedBonusesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Long-Term Incentive Compensation Payable</link:label>
    <link:label id="lab_bur_ScheduleOfAccruedBonusesTableTextBlock_label_en-US" xlink:label="lab_bur_ScheduleOfAccruedBonusesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Accrued Bonuses [Table Text Block]</link:label>
    <link:label id="lab_bur_ScheduleOfAccruedBonusesTableTextBlock_documentation_en-US" xlink:label="lab_bur_ScheduleOfAccruedBonusesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tabular disclosure of changes in long term incentive compensation payable.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ScheduleOfAccruedBonusesTableTextBlock" xlink:href="bur-20260630.xsd#bur_ScheduleOfAccruedBonusesTableTextBlock"/>
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    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019e415a-4dba-7737-9c19-0a8d7967d228_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial commitments and contingent liabilities</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_019e415a-4dba-7601-963f-68ed283f7e0c_verboseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Potential ordinary shares excluded from diluted weighted average ordinary shares (in shares)</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_UnsecuredNotes6.250PercentDueApril2028Member_019e415a-4e63-7aea-b261-dd1f685bdd23_terseLabel_en-US" xlink:label="lab_bur_UnsecuredNotes6.250PercentDueApril2028Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">6.250% Senior Notes due 2028</link:label>
    <link:label id="lab_bur_UnsecuredNotes6.250PercentDueApril2028Member_label_en-US" xlink:label="lab_bur_UnsecuredNotes6.250PercentDueApril2028Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Notes 6.250 Percent Due April 2028 [Member]</link:label>
    <link:label id="lab_bur_UnsecuredNotes6.250PercentDueApril2028Member_documentation_en-US" xlink:label="lab_bur_UnsecuredNotes6.250PercentDueApril2028Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents information pertaining to unsecured Notes 6.250 Percent Due April 2028.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_UnsecuredNotes6.250PercentDueApril2028Member" xlink:href="bur-20260630.xsd#bur_UnsecuredNotes6.250PercentDueApril2028Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_UnsecuredNotes6.250PercentDueApril2028Member" xlink:to="lab_bur_UnsecuredNotes6.250PercentDueApril2028Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019e415a-4dba-789e-999a-8675745878e1_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_WeightedAverageMember_019e415a-4e63-72b9-a53d-f6e6661edb4c_terseLabel_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average</link:label>
    <link:label id="lab_srt_WeightedAverageMember_label_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_WeightedAverageMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_WeightedAverageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_WeightedAverageMember" xlink:to="lab_srt_WeightedAverageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e415a-4e63-7b40-8d5a-973ac9e0a4b0_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by/(used in) operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableMember_019e415a-4e63-74da-b72b-d2df7f8c075e_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from settlement of capital provision assets</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableMember_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableMember" xlink:to="lab_us-gaap_AccountsReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDerivativeLiabilities_019e415a-4dba-7f44-9ba8-a6c199a7a18d_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net increase/(decrease) on financial liability to third-party investment</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Derivative Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInDerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDerivativeLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInDerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_VariableInterestEntityOffBalanceSheetExposure_019e415a-4e63-76d5-a994-e9b677a391a3_terseLabel_en-US" xlink:label="lab_bur_VariableInterestEntityOffBalanceSheetExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Off-balance sheet exposure - undrawn commitments</link:label>
    <link:label id="lab_bur_VariableInterestEntityOffBalanceSheetExposure_label_en-US" xlink:label="lab_bur_VariableInterestEntityOffBalanceSheetExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Off Balance Sheet Exposure</link:label>
    <link:label id="lab_bur_VariableInterestEntityOffBalanceSheetExposure_documentation_en-US" xlink:label="lab_bur_VariableInterestEntityOffBalanceSheetExposure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The amount of off balance sheet undrawn commitments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_VariableInterestEntityOffBalanceSheetExposure" xlink:href="bur-20260630.xsd#bur_VariableInterestEntityOffBalanceSheetExposure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_VariableInterestEntityOffBalanceSheetExposure" xlink:to="lab_bur_VariableInterestEntityOffBalanceSheetExposure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019e415a-4dba-78a5-9fba-8e0e70fedeed_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019e415a-4e63-7916-85ae-1dcd33ccd08d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AdjustmentsToAdditionalPaidInCapitalRetainedEarningsShareBasedPaymentArrangement_019e415a-4e63-76f8-b097-f57009f469b8_terseLabel_en-US" xlink:label="lab_bur_AdjustmentsToAdditionalPaidInCapitalRetainedEarningsShareBasedPaymentArrangement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer of share-based awards and NQDC Plan matching awards on vesting</link:label>
    <link:label id="lab_bur_AdjustmentsToAdditionalPaidInCapitalRetainedEarningsShareBasedPaymentArrangement_label_en-US" xlink:label="lab_bur_AdjustmentsToAdditionalPaidInCapitalRetainedEarningsShareBasedPaymentArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments To Additional Paid-In-Capital, Retained Earnings, Share-Based Payment Arrangement</link:label>
    <link:label id="lab_bur_AdjustmentsToAdditionalPaidInCapitalRetainedEarningsShareBasedPaymentArrangement_documentation_en-US" xlink:label="lab_bur_AdjustmentsToAdditionalPaidInCapitalRetainedEarningsShareBasedPaymentArrangement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjustments To Additional Paid-In-Capital, Retained Earnings, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AdjustmentsToAdditionalPaidInCapitalRetainedEarningsShareBasedPaymentArrangement" xlink:href="bur-20260630.xsd#bur_AdjustmentsToAdditionalPaidInCapitalRetainedEarningsShareBasedPaymentArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AdjustmentsToAdditionalPaidInCapitalRetainedEarningsShareBasedPaymentArrangement" xlink:to="lab_bur_AdjustmentsToAdditionalPaidInCapitalRetainedEarningsShareBasedPaymentArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_019e415a-4dba-7afd-bf79-7e2f65362188_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax asset</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:to="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalariesWagesAndOfficersCompensation_019e415a-4dba-7559-8d1f-419d26eb6405_terseLabel_en-US" xlink:label="lab_us-gaap_SalariesWagesAndOfficersCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Salaries and benefits</link:label>
    <link:label id="lab_us-gaap_SalariesWagesAndOfficersCompensation_label_en-US" xlink:label="lab_us-gaap_SalariesWagesAndOfficersCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Salary and Wage, Excluding Cost of Good and Service Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalariesWagesAndOfficersCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SalariesWagesAndOfficersCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalariesWagesAndOfficersCompensation" xlink:to="lab_us-gaap_SalariesWagesAndOfficersCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_019e415a-4e64-7d81-b360-789e3e53b6d0_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingAfterYearFive_019e415a-4dba-7225-ac17-2d779ce15029_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments of Principal in Rolling after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingAfterYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsLegalRiskManagementMember_019e415a-4dba-780e-94b6-49036ba586a6_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsLegalRiskManagementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal risk management</link:label>
    <link:label id="lab_bur_DerivativeAssetsLegalRiskManagementMember_label_en-US" xlink:label="lab_bur_DerivativeAssetsLegalRiskManagementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets, Legal Risk Management [Member]</link:label>
    <link:label id="lab_bur_DerivativeAssetsLegalRiskManagementMember_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsLegalRiskManagementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to capital provision assets legal risk management.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsLegalRiskManagementMember" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsLegalRiskManagementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsLegalRiskManagementMember" xlink:to="lab_bur_DerivativeAssetsLegalRiskManagementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019e415a-4e63-7609-a27c-2f82cbdb81c7_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019e415a-4e63-7213-8547-0de8c9ee810d_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income/(loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsPortfolioMember_019e415a-4dba-7561-8b2c-020760768727_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsPortfolioMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portfolio</link:label>
    <link:label id="lab_bur_DerivativeAssetsPortfolioMember_label_en-US" xlink:label="lab_bur_DerivativeAssetsPortfolioMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets, Portfolio [Member]</link:label>
    <link:label id="lab_bur_DerivativeAssetsPortfolioMember_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsPortfolioMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to capital provision assets portfolio.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsPortfolioMember" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsPortfolioMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsPortfolioMember" xlink:to="lab_bur_DerivativeAssetsPortfolioMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_019e415a-4dba-7f99-96b7-2e8ebae9ec63_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent events</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_019e415a-4dba-78ff-853e-e7871c5bed4f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFairValue" xlink:to="lab_us-gaap_DebtInstrumentFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019e415a-4dba-73c8-8c3a-e7772f7aa03f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_019e415a-4e63-7274-99bf-768d1cb95492_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019e415a-4dba-7f29-9b78-8d6a3523dd46_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_019e415a-4dba-7bca-82d8-97bd1cce6d97_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_019e415a-4dba-78e0-9cfb-f904d7ca2219_verboseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019e415a-4e63-7829-96c1-1d7f714815c4_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccruedBonusesTextBlock_019e415a-4dba-70d9-befd-42a24d3e3bd2_terseLabel_en-US" xlink:label="lab_bur_AccruedBonusesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term incentive compensation payable</link:label>
    <link:label id="lab_bur_AccruedBonusesTextBlock_label_en-US" xlink:label="lab_bur_AccruedBonusesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Bonuses [Text Block]</link:label>
    <link:label id="lab_bur_AccruedBonusesTextBlock_documentation_en-US" xlink:label="lab_bur_AccruedBonusesTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The disclosure of long term incentive compensation.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccruedBonusesTextBlock" xlink:href="bur-20260630.xsd#bur_AccruedBonusesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccruedBonusesTextBlock" xlink:to="lab_bur_AccruedBonusesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_019e415a-4dba-72b1-8562-0ea824e48618_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceBurfordOpportunityFundCLpMember_019e415a-4e63-787b-aeb6-494dffa894e9_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceBurfordOpportunityFundCLpMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Core legal finance (BOF-C)</link:label>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceBurfordOpportunityFundCLpMember_label_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceBurfordOpportunityFundCLpMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets Core Legal Finance Burford Opportunity Fund C Lp [Member]</link:label>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceBurfordOpportunityFundCLpMember_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceBurfordOpportunityFundCLpMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to capital provision assets, core legal finance (BOF-C)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsCoreLegalFinanceBurfordOpportunityFundCLpMember" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsCoreLegalFinanceBurfordOpportunityFundCLpMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsCoreLegalFinanceBurfordOpportunityFundCLpMember" xlink:to="lab_bur_DerivativeAssetsCoreLegalFinanceBurfordOpportunityFundCLpMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_019e415a-4dba-7d0b-8c47-83dbd7a2d12a_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">VIE not primary beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_IncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseIncreaseInInterestRate_019e415a-4e64-7efc-9a3d-60a41383b9db_terseLabel_en-US" xlink:label="lab_bur_IncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseIncreaseInInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in income and net assets due to decrease in interest rate</link:label>
    <link:label id="lab_bur_IncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseIncreaseInInterestRate_label_en-US" xlink:label="lab_bur_IncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseIncreaseInInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Consolidated Income And Net Assets Due To (Decrease) Increase In Interest Rate</link:label>
    <link:label id="lab_bur_IncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseIncreaseInInterestRate_documentation_en-US" xlink:label="lab_bur_IncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseIncreaseInInterestRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Consolidated Income And Net Assets Due To (Decrease) Increase In Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_IncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseIncreaseInInterestRate" xlink:href="bur-20260630.xsd#bur_IncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseIncreaseInInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_IncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseIncreaseInInterestRate" xlink:to="lab_bur_IncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseIncreaseInInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_019e415a-4e63-781b-8bec-75b02250b7d1_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_019e415a-4dba-7b33-a703-c25cd0d99aa9_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Finance costs</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_019e415a-4dba-7348-9d51-04607e2d05df_totalLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total finance costs</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseNonoperating" xlink:to="lab_us-gaap_InterestExpenseNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetAssetLiability_019e415a-4e63-7c5d-8d2e-4b930c6d9fa8_totalLabel_en-US" xlink:label="lab_us-gaap_FairValueNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net total</link:label>
    <link:label id="lab_us-gaap_FairValueNetAssetLiability_019e415a-4e63-7e0a-91c8-4716eba062d4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset (liability) fair value</link:label>
    <link:label id="lab_us-gaap_FairValueNetAssetLiability_label_en-US" xlink:label="lab_us-gaap_FairValueNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Asset (Liability)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetAssetLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueNetAssetLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetAssetLiability" xlink:to="lab_us-gaap_FairValueNetAssetLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_019e415a-4e63-76f9-9d82-fce18c872454_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">(Increase)/decrease in other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DefinitiveUndrawnCommitments_019e415a-4e63-7e47-9820-8d21be19e734_terseLabel_en-US" xlink:label="lab_bur_DefinitiveUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Definitive</link:label>
    <link:label id="lab_bur_DefinitiveUndrawnCommitments_label_en-US" xlink:label="lab_bur_DefinitiveUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Definitive Undrawn Commitments</link:label>
    <link:label id="lab_bur_DefinitiveUndrawnCommitments_documentation_en-US" xlink:label="lab_bur_DefinitiveUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The amount of definitive undrawn commitments as at the end of the reporting period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DefinitiveUndrawnCommitments" xlink:href="bur-20260630.xsd#bur_DefinitiveUndrawnCommitments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DefinitiveUndrawnCommitments" xlink:to="lab_bur_DefinitiveUndrawnCommitments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilities_019e415a-4dba-76f4-9498-80a415ef0640_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net deferred tax liabilities</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilities" xlink:to="lab_us-gaap_DeferredTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditLossFinancialInstrumentTextBlock_019e415a-4dba-7534-a9db-d22e970cd955_terseLabel_en-US" xlink:label="lab_us-gaap_CreditLossFinancialInstrumentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit risk from financial instruments</link:label>
    <link:label id="lab_us-gaap_CreditLossFinancialInstrumentTextBlock_label_en-US" xlink:label="lab_us-gaap_CreditLossFinancialInstrumentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Loss, Financial Instrument [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditLossFinancialInstrumentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditLossFinancialInstrumentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditLossFinancialInstrumentTextBlock" xlink:to="lab_us-gaap_CreditLossFinancialInstrumentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccruedBonusesRollForward_019e415a-4dba-76d7-824b-931025ccc76a_terseLabel_en-US" xlink:label="lab_bur_AccruedBonusesRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued Bonuses [Roll Forward]</link:label>
    <link:label id="lab_bur_AccruedBonusesRollForward_label_en-US" xlink:label="lab_bur_AccruedBonusesRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Bonuses [Roll Forward]</link:label>
    <link:label id="lab_bur_AccruedBonusesRollForward_documentation_en-US" xlink:label="lab_bur_AccruedBonusesRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Bonuses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccruedBonusesRollForward" xlink:href="bur-20260630.xsd#bur_AccruedBonusesRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccruedBonusesRollForward" xlink:to="lab_bur_AccruedBonusesRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_019e415a-4dba-7459-83ba-3a75ac34d27b_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based and deferred compensation</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_NonDerivativeAssetsFairValueDisclosure_019e415a-4dba-7de9-8f72-49ab8d539b4b_terseLabel_en-US" xlink:label="lab_bur_NonDerivativeAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-derivative financial assets</link:label>
    <link:label id="lab_bur_NonDerivativeAssetsFairValueDisclosure_label_en-US" xlink:label="lab_bur_NonDerivativeAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Derivative Assets, Fair Value Disclosure</link:label>
    <link:label id="lab_bur_NonDerivativeAssetsFairValueDisclosure_documentation_en-US" xlink:label="lab_bur_NonDerivativeAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Derivative Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_NonDerivativeAssetsFairValueDisclosure" xlink:href="bur-20260630.xsd#bur_NonDerivativeAssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_NonDerivativeAssetsFairValueDisclosure" xlink:to="lab_bur_NonDerivativeAssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_019e415a-4dba-7c0a-a3fe-d2d3e1cf723f_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesUnrealizedGainLoss_019e415a-4e63-73c9-a749-ed7fb2636998_terseLabel_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets of consolidated investment companies, Unrealized</link:label>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesUnrealizedGainLoss_label_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Of Consolidated Investment Companies, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesUnrealizedGainLoss_documentation_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets Of Consolidated Investment Companies, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AssetsOfConsolidatedInvestmentCompaniesUnrealizedGainLoss" xlink:href="bur-20260630.xsd#bur_AssetsOfConsolidatedInvestmentCompaniesUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AssetsOfConsolidatedInvestmentCompaniesUnrealizedGainLoss" xlink:to="lab_bur_AssetsOfConsolidatedInvestmentCompaniesUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetTransfers_019e415a-4dba-7561-9ede-7129e1c33ed0_negatedTerseLabel_en-US" xlink:label="lab_bur_DerivativeAssetTransfers" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfers</link:label>
    <link:label id="lab_bur_DerivativeAssetTransfers_label_en-US" xlink:label="lab_bur_DerivativeAssetTransfers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Transfers</link:label>
    <link:label id="lab_bur_DerivativeAssetTransfers_documentation_en-US" xlink:label="lab_bur_DerivativeAssetTransfers" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Asset, Transfers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetTransfers" xlink:href="bur-20260630.xsd#bur_DerivativeAssetTransfers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetTransfers" xlink:to="lab_bur_DerivativeAssetTransfers" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ManagementFeeIncomeMember_019e415a-4dba-7ed0-a91a-ffa6ab43730e_verboseLabel_en-US" xlink:label="lab_bur_ManagementFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Management fee income</link:label>
    <link:label id="lab_bur_ManagementFeeIncomeMember_label_en-US" xlink:label="lab_bur_ManagementFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fee Income [Member]</link:label>
    <link:label id="lab_bur_ManagementFeeIncomeMember_documentation_en-US" xlink:label="lab_bur_ManagementFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents information pertaining to management fees.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ManagementFeeIncomeMember" xlink:href="bur-20260630.xsd#bur_ManagementFeeIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ManagementFeeIncomeMember" xlink:to="lab_bur_ManagementFeeIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputCollectionRiskMember_019e415a-4e63-7731-af5d-bf6c3f37edae_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputCollectionRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collection risk</link:label>
    <link:label id="lab_bur_MeasurementInputCollectionRiskMember_label_en-US" xlink:label="lab_bur_MeasurementInputCollectionRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Collection Risk [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputCollectionRiskMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputCollectionRiskMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using collection risk.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputCollectionRiskMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputCollectionRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputCollectionRiskMember" xlink:to="lab_bur_MeasurementInputCollectionRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_label_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PayablesAndAccrualsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:to="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_019e415a-4e63-70c4-aba8-32dbfee1d204_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpenses_019e415a-4dba-7f5a-a90e-9e15569a55e7_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total operating expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpenses" xlink:to="lab_us-gaap_OperatingExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_019e415a-4e63-76a8-b243-b9b8a2f604f4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Key Unobservable Inputs</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019e415a-4dba-7e13-b844-898cbf066cf8_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in equity</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019e415a-4dba-7ce6-b6f6-592ffe2ed873_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ordinary shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_019e415a-4dba-7a6c-9c27-a5b7300bb096_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_019e415a-4dba-7dda-b82f-f5d3d93962c1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019e415a-4e63-7401-9102-f85b133724a3_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019e415a-4e63-79c4-9d28-5320b1315e3f_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FinancialInstrumentDecreaseInExpectedTimingOfAFavorableOutcome_019e415a-4e63-7263-8782-aa8f5e34658e_terseLabel_en-US" xlink:label="lab_bur_FinancialInstrumentDecreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Decrease in expected timing of a favorable outcome</link:label>
    <link:label id="lab_bur_FinancialInstrumentDecreaseInExpectedTimingOfAFavorableOutcome_label_en-US" xlink:label="lab_bur_FinancialInstrumentDecreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument, Decrease In Expected Timing Of A Favorable Outcome</link:label>
    <link:label id="lab_bur_FinancialInstrumentDecreaseInExpectedTimingOfAFavorableOutcome_documentation_en-US" xlink:label="lab_bur_FinancialInstrumentDecreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the decrease in expected timing of a favorable outcome.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FinancialInstrumentDecreaseInExpectedTimingOfAFavorableOutcome" xlink:href="bur-20260630.xsd#bur_FinancialInstrumentDecreaseInExpectedTimingOfAFavorableOutcome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FinancialInstrumentDecreaseInExpectedTimingOfAFavorableOutcome" xlink:to="lab_bur_FinancialInstrumentDecreaseInExpectedTimingOfAFavorableOutcome" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_UnsecuredNotes9.250PercentDueJuly2031Member_019e415a-4dba-708d-8ad8-7d150b42f4d9_terseLabel_en-US" xlink:label="lab_bur_UnsecuredNotes9.250PercentDueJuly2031Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">9.250% Senior Notes due 2031</link:label>
    <link:label id="lab_bur_UnsecuredNotes9.250PercentDueJuly2031Member_label_en-US" xlink:label="lab_bur_UnsecuredNotes9.250PercentDueJuly2031Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Notes 9.250 Percent Due July 2031 [Member]</link:label>
    <link:label id="lab_bur_UnsecuredNotes9.250PercentDueJuly2031Member_documentation_en-US" xlink:label="lab_bur_UnsecuredNotes9.250PercentDueJuly2031Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to 9.250% senior notes due July 2031.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_UnsecuredNotes9.250PercentDueJuly2031Member" xlink:href="bur-20260630.xsd#bur_UnsecuredNotes9.250PercentDueJuly2031Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_UnsecuredNotes9.250PercentDueJuly2031Member" xlink:to="lab_bur_UnsecuredNotes9.250PercentDueJuly2031Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccruedContingentFees_019e415a-4dba-7075-998c-e1093a9c9ae6_terseLabel_en-US" xlink:label="lab_bur_AccruedContingentFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent fees</link:label>
    <link:label id="lab_bur_AccruedContingentFees_label_en-US" xlink:label="lab_bur_AccruedContingentFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Contingent Fees</link:label>
    <link:label id="lab_bur_AccruedContingentFees_documentation_en-US" xlink:label="lab_bur_AccruedContingentFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Contingent Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccruedContingentFees" xlink:href="bur-20260630.xsd#bur_AccruedContingentFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccruedContingentFees" xlink:to="lab_bur_AccruedContingentFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e415a-4dba-7bcf-9e22-f44600680f53_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by/(used in) financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CountryRegion_019e415a-4dba-7651-880b-76cc7faeafcb_terseLabel_en-US" xlink:label="lab_dei_CountryRegion" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Country Region</link:label>
    <link:label id="lab_dei_CountryRegion_label_en-US" xlink:label="lab_dei_CountryRegion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Country Region</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CountryRegion" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CountryRegion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CountryRegion" xlink:to="lab_dei_CountryRegion" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_019e415a-4e63-7782-af92-37ede0b2df4a_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value adjustment during the period, net of previously recognized unrealized gains/(losses) transferred to realized gains/(losses)</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnInvestments" xlink:to="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetManagement1Member_019e415a-4e63-7722-9040-ab70b4ba4760_terseLabel_en-US" xlink:label="lab_us-gaap_AssetManagement1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset management income/(loss)</link:label>
    <link:label id="lab_us-gaap_AssetManagement1Member_label_en-US" xlink:label="lab_us-gaap_AssetManagement1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetManagement1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetManagement1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetManagement1Member" xlink:to="lab_us-gaap_AssetManagement1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInInterestRate_019e415a-4dba-7dd5-af8b-3bd247e1a4f9_negatedLabel_en-US" xlink:label="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInInterestRate" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Decrease in income and net assets due to increase in interest rate</link:label>
    <link:label id="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInInterestRate_label_en-US" xlink:label="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Decrease In Consolidated Income And Net Assets Due To Increase In Interest Rate</link:label>
    <link:label id="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInInterestRate_documentation_en-US" xlink:label="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInInterestRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Decrease in income and assets due to increase in interest rate of capital provision assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInInterestRate" xlink:href="bur-20260630.xsd#bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInInterestRate" xlink:to="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019e415a-4dba-722d-9914-427607bca9ba_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income/(loss) to net cash provided by/(used in) operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_CapitalProvisionAssetsPayable_019e415a-4e63-7b05-aaaa-4157c7baa02a_terseLabel_en-US" xlink:label="lab_bur_CapitalProvisionAssetsPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payable for capital provision assets</link:label>
    <link:label id="lab_bur_CapitalProvisionAssetsPayable_label_en-US" xlink:label="lab_bur_CapitalProvisionAssetsPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Provision Assets, Payable</link:label>
    <link:label id="lab_bur_CapitalProvisionAssetsPayable_documentation_en-US" xlink:label="lab_bur_CapitalProvisionAssetsPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Obligations from capital provision assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_CapitalProvisionAssetsPayable" xlink:href="bur-20260630.xsd#bur_CapitalProvisionAssetsPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_CapitalProvisionAssetsPayable" xlink:to="lab_bur_CapitalProvisionAssetsPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019e415a-4e63-7e1e-9e0e-d14c2184f692_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019e415a-4dba-73b9-adf3-160b77edb32f_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset management income/(loss)</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputAppealJudgmentMember_019e415a-4dba-7ea3-9e6f-c4cc97f7379b_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputAppealJudgmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Appeal judgment</link:label>
    <link:label id="lab_bur_MeasurementInputAppealJudgmentMember_label_en-US" xlink:label="lab_bur_MeasurementInputAppealJudgmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Appeal Judgment [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputAppealJudgmentMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputAppealJudgmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using appeal judgment.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputAppealJudgmentMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputAppealJudgmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputAppealJudgmentMember" xlink:to="lab_bur_MeasurementInputAppealJudgmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_019e415a-4e63-738c-ac6c-c1a3b18ccec4_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputResolutionTimingMember_019e415a-4e64-777a-9147-6e413d1d0ac5_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputResolutionTimingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Resolution timing (years)</link:label>
    <link:label id="lab_bur_MeasurementInputResolutionTimingMember_label_en-US" xlink:label="lab_bur_MeasurementInputResolutionTimingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Resolution Timing [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputResolutionTimingMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputResolutionTimingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using resolution timing.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputResolutionTimingMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputResolutionTimingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputResolutionTimingMember" xlink:to="lab_bur_MeasurementInputResolutionTimingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ScheduleOfIncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToChangeInActualInterestRatesUsedInFairValueEstimationTableTextBlock_019e415a-4dba-7e28-93b2-9b02e5988060_terseLabel_en-US" xlink:label="lab_bur_ScheduleOfIncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToChangeInActualInterestRatesUsedInFairValueEstimationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Increase (Decrease) in Consolidated Income and Net Assets Due to Change in Actual Interest Rates</link:label>
    <link:label id="lab_bur_ScheduleOfIncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToChangeInActualInterestRatesUsedInFairValueEstimationTableTextBlock_label_en-US" xlink:label="lab_bur_ScheduleOfIncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToChangeInActualInterestRatesUsedInFairValueEstimationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Increase (Decrease) In Consolidated Income And Net Assets due to Change In Actual Interest Rates Used In Fair Value Estimation [Table Text Block]</link:label>
    <link:label id="lab_bur_ScheduleOfIncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToChangeInActualInterestRatesUsedInFairValueEstimationTableTextBlock_documentation_en-US" xlink:label="lab_bur_ScheduleOfIncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToChangeInActualInterestRatesUsedInFairValueEstimationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of increase (decrease) in consolidated income and net assets due to change in actual interest rates used in fair value estimation.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ScheduleOfIncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToChangeInActualInterestRatesUsedInFairValueEstimationTableTextBlock" xlink:href="bur-20260630.xsd#bur_ScheduleOfIncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToChangeInActualInterestRatesUsedInFairValueEstimationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ScheduleOfIncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToChangeInActualInterestRatesUsedInFairValueEstimationTableTextBlock" xlink:to="lab_bur_ScheduleOfIncreaseDecreaseInConsolidatedIncomeAndNetAssetsDueToChangeInActualInterestRatesUsedInFairValueEstimationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_019e415a-4e63-7844-94bb-f3f621a8c21e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital provision assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_019e415a-4e63-791a-b014-4353f12069d5_periodStartLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning of period</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_019e415a-4e63-73f4-b374-3171814cf065_periodEndLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">End of period</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_019e415a-4e63-7e44-aca6-d1ece1a88a56_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total capital provision assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_019e415a-4e63-7ce0-ac5b-7bb168915474_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Derivative financial assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncome_019e415a-4e63-7cd6-9c80-f4febb4ed03e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherIncome_019e415a-4e63-780d-8f71-64f7fb4614cb_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherIncome" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other (income)/loss</link:label>
    <link:label id="lab_us-gaap_OtherIncome_label_en-US" xlink:label="lab_us-gaap_OtherIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncome" xlink:to="lab_us-gaap_OtherIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccruedGeneralExpenses_019e415a-4e63-7644-acdc-7c48a72b4384_terseLabel_en-US" xlink:label="lab_bur_AccruedGeneralExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General expenses payable</link:label>
    <link:label id="lab_bur_AccruedGeneralExpenses_label_en-US" xlink:label="lab_bur_AccruedGeneralExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued General Expenses</link:label>
    <link:label id="lab_bur_AccruedGeneralExpenses_documentation_en-US" xlink:label="lab_bur_AccruedGeneralExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Carrying value as of the balance sheet date of obligations incurred through that date and payable for general expenses.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccruedGeneralExpenses" xlink:href="bur-20260630.xsd#bur_AccruedGeneralExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccruedGeneralExpenses" xlink:to="lab_bur_AccruedGeneralExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_019e415a-4e63-71a8-bab2-48e5c7abf057_terseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Plus)/Less: Comprehensive income/(loss) attributable to non-controlling interests</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_019e415a-4e64-7c4b-a81b-60380e4fe0d4_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset management income</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ScheduleOfIncreaseOrDecreaseInConsolidatedIncomeOrNetAssetsDueToExpectedTimingOfFavorableOutcomeTableTextBlock_019e415a-4dba-7033-a597-e5684dfc2d14_terseLabel_en-US" xlink:label="lab_bur_ScheduleOfIncreaseOrDecreaseInConsolidatedIncomeOrNetAssetsDueToExpectedTimingOfFavorableOutcomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Increase (Decrease) in Consolidated Income or Net Assets Due to Expected Timing of Favorable Outcome</link:label>
    <link:label id="lab_bur_ScheduleOfIncreaseOrDecreaseInConsolidatedIncomeOrNetAssetsDueToExpectedTimingOfFavorableOutcomeTableTextBlock_label_en-US" xlink:label="lab_bur_ScheduleOfIncreaseOrDecreaseInConsolidatedIncomeOrNetAssetsDueToExpectedTimingOfFavorableOutcomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Increase Or Decrease In Consolidated Income Or Net Assets Due To Expected Timing Of Favorable Outcome [Table Text Block]</link:label>
    <link:label id="lab_bur_ScheduleOfIncreaseOrDecreaseInConsolidatedIncomeOrNetAssetsDueToExpectedTimingOfFavorableOutcomeTableTextBlock_documentation_en-US" xlink:label="lab_bur_ScheduleOfIncreaseOrDecreaseInConsolidatedIncomeOrNetAssetsDueToExpectedTimingOfFavorableOutcomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of increase (decrease) in consolidated income or net assets due to expected timing of favorable outcome.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ScheduleOfIncreaseOrDecreaseInConsolidatedIncomeOrNetAssetsDueToExpectedTimingOfFavorableOutcomeTableTextBlock" xlink:href="bur-20260630.xsd#bur_ScheduleOfIncreaseOrDecreaseInConsolidatedIncomeOrNetAssetsDueToExpectedTimingOfFavorableOutcomeTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ScheduleOfIncreaseOrDecreaseInConsolidatedIncomeOrNetAssetsDueToExpectedTimingOfFavorableOutcomeTableTextBlock" xlink:to="lab_bur_ScheduleOfIncreaseOrDecreaseInConsolidatedIncomeOrNetAssetsDueToExpectedTimingOfFavorableOutcomeTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_019e415a-4dba-7916-a821-eaaad8acdf06_negatedLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Realizations</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ForeignExchangeGainLossesOnAccountsReceivableHeldAtFairValue_019e415a-4e64-7f23-b4ec-9291693d3e2b_terseLabel_en-US" xlink:label="lab_bur_ForeignExchangeGainLossesOnAccountsReceivableHeldAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange gains/(losses)</link:label>
    <link:label id="lab_bur_ForeignExchangeGainLossesOnAccountsReceivableHeldAtFairValue_label_en-US" xlink:label="lab_bur_ForeignExchangeGainLossesOnAccountsReceivableHeldAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Exchange Gain (Losses) On Accounts Receivable, Held At Fair Value</link:label>
    <link:label id="lab_bur_ForeignExchangeGainLossesOnAccountsReceivableHeldAtFairValue_documentation_en-US" xlink:label="lab_bur_ForeignExchangeGainLossesOnAccountsReceivableHeldAtFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of foreign exchange gain (loss) on due from settlement of capital provision assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ForeignExchangeGainLossesOnAccountsReceivableHeldAtFairValue" xlink:href="bur-20260630.xsd#bur_ForeignExchangeGainLossesOnAccountsReceivableHeldAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ForeignExchangeGainLossesOnAccountsReceivableHeldAtFairValue" xlink:to="lab_bur_ForeignExchangeGainLossesOnAccountsReceivableHeldAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ProceedsFromJointVenturesAndEquityMethodInvestments_019e415a-4e63-7678-914c-94eb727e7912_terseLabel_en-US" xlink:label="lab_bur_ProceedsFromJointVenturesAndEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from joint ventures and equity method investments</link:label>
    <link:label id="lab_bur_ProceedsFromJointVenturesAndEquityMethodInvestments_label_en-US" xlink:label="lab_bur_ProceedsFromJointVenturesAndEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Joint Ventures And Equity Method Investments</link:label>
    <link:label id="lab_bur_ProceedsFromJointVenturesAndEquityMethodInvestments_documentation_en-US" xlink:label="lab_bur_ProceedsFromJointVenturesAndEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The cash inflow from investment in joint ventures and equity method investments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ProceedsFromJointVenturesAndEquityMethodInvestments" xlink:href="bur-20260630.xsd#bur_ProceedsFromJointVenturesAndEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ProceedsFromJointVenturesAndEquityMethodInvestments" xlink:to="lab_bur_ProceedsFromJointVenturesAndEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesForeignExchangeGainsLosses_019e415a-4e64-747b-96e2-847d954e921e_terseLabel_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesForeignExchangeGainsLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange gains/(losses)</link:label>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesForeignExchangeGainsLosses_label_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesForeignExchangeGainsLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Liabilities, Foreign Exchange Gains (Losses)</link:label>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesForeignExchangeGainsLosses_documentation_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesForeignExchangeGainsLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Liabilities, Foreign Exchange Gains (Losses)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesForeignExchangeGainsLosses" xlink:href="bur-20260630.xsd#bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesForeignExchangeGainsLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesForeignExchangeGainsLosses" xlink:to="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitiesForeignExchangeGainsLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetCost_019e415a-4e63-779e-8087-4114b838672d_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deployed cost, end of period</link:label>
    <link:label id="lab_bur_DerivativeAssetCost_label_en-US" xlink:label="lab_bur_DerivativeAssetCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Cost</link:label>
    <link:label id="lab_bur_DerivativeAssetCost_documentation_en-US" xlink:label="lab_bur_DerivativeAssetCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Asset, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetCost" xlink:href="bur-20260630.xsd#bur_DerivativeAssetCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetCost" xlink:to="lab_bur_DerivativeAssetCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019e415a-4e63-76a7-9507-49b38d6470e3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AssetManagementAndOtherServicesMember_019e415a-4e63-7af2-bce7-91f5cb5ca4e0_terseLabel_en-US" xlink:label="lab_bur_AssetManagementAndOtherServicesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Management and Other Services</link:label>
    <link:label id="lab_bur_AssetManagementAndOtherServicesMember_label_en-US" xlink:label="lab_bur_AssetManagementAndOtherServicesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management And Other Services [Member]</link:label>
    <link:label id="lab_bur_AssetManagementAndOtherServicesMember_documentation_en-US" xlink:label="lab_bur_AssetManagementAndOtherServicesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to asset Management and Other services.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AssetManagementAndOtherServicesMember" xlink:href="bur-20260630.xsd#bur_AssetManagementAndOtherServicesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AssetManagementAndOtherServicesMember" xlink:to="lab_bur_AssetManagementAndOtherServicesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_019e415a-4dba-7176-8df6-cc0636f8bc0d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019e415a-4e63-7061-ab3b-ca5977a4b1a9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_JointVenturesAndEquityMethodInvestmentsMember_019e415a-4dba-7578-a9fd-d06a897660f2_terseLabel_en-US" xlink:label="lab_bur_JointVenturesAndEquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Joint ventures and equity method investments</link:label>
    <link:label id="lab_bur_JointVenturesAndEquityMethodInvestmentsMember_label_en-US" xlink:label="lab_bur_JointVenturesAndEquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Joint Ventures And Equity Method Investments [Member]</link:label>
    <link:label id="lab_bur_JointVenturesAndEquityMethodInvestmentsMember_documentation_en-US" xlink:label="lab_bur_JointVenturesAndEquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to joint ventures and equity method investments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_JointVenturesAndEquityMethodInvestmentsMember" xlink:href="bur-20260630.xsd#bur_JointVenturesAndEquityMethodInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_JointVenturesAndEquityMethodInvestmentsMember" xlink:to="lab_bur_JointVenturesAndEquityMethodInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract_019e415a-4dba-77f9-9c49-612bad74b001_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other expenses</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNonoperatingIncomeExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_019e415a-4e63-7ac7-8aba-c54019a27ac1_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_019e415a-4e63-788b-a5f4-b894d01e39fa_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">End of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_019e415a-4dba-7e21-a6a5-15f39b9833b5_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Operating income/(loss)</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_LongTermDebtInterestRollingMaturityAbstract_019e415a-4e63-7dcf-8efc-0beb56c5caa9_terseLabel_en-US" xlink:label="lab_bur_LongTermDebtInterestRollingMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt interest payable</link:label>
    <link:label id="lab_bur_LongTermDebtInterestRollingMaturityAbstract_label_en-US" xlink:label="lab_bur_LongTermDebtInterestRollingMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Interest, Rolling Maturity [Abstract]</link:label>
    <link:label id="lab_bur_LongTermDebtInterestRollingMaturityAbstract_documentation_en-US" xlink:label="lab_bur_LongTermDebtInterestRollingMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Interest, Rolling Maturity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_LongTermDebtInterestRollingMaturityAbstract" xlink:href="bur-20260630.xsd#bur_LongTermDebtInterestRollingMaturityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_LongTermDebtInterestRollingMaturityAbstract" xlink:to="lab_bur_LongTermDebtInterestRollingMaturityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_019e415a-4dba-7ac3-afd0-5712de66c5c0_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfDebt_019e415a-4e63-7909-b2cb-e7dadc857a9e_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance, including original issue premium</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueNoncurrent_019e415a-4e63-7d58-80e1-6b22066ae42b_terseLabel_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-current assets</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueNoncurrent_label_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Held At Fair Value, Noncurrent</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueNoncurrent_documentation_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueNoncurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due from settlement of capital provision assets carrying amounts as of the balance sheet date of all assets that are expected to be realized in cash, sold or consumed after one year or beyond the normal operating cycle, if longer.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccountsReceivableHeldAtFairValueNoncurrent" xlink:href="bur-20260630.xsd#bur_AccountsReceivableHeldAtFairValueNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccountsReceivableHeldAtFairValueNoncurrent" xlink:to="lab_bur_AccountsReceivableHeldAtFairValueNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember_019e415a-4dba-7570-8d65-46e58c02ae31_verboseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Lower risk legal finance (Advantage Fund)</link:label>
    <link:label id="lab_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember_019e415a-4dba-7442-bca8-79654d275c17_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lower risk legal finance (Advantage Fund)</link:label>
    <link:label id="lab_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember_label_en-US" xlink:label="lab_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets, Lower Risk Legal Finance Advantage Fund [Member]</link:label>
    <link:label id="lab_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to capital provision assets, lower risk legal finance (advantage fund).</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember" xlink:to="lab_bur_DerivativeAssetsLowerRiskLegalFinanceAdvantageFundMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_019e415a-4e63-7c46-ba37-798bb9634b99_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_019e415a-4e63-7e14-ba8f-3336ef65401f_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_019e415a-4e63-7dfb-84a6-f09b0c430773_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of new ordinary shares to satisfy distributions under the NQDC Plan</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_InterestRateChangeOf100BpsMember_019e415a-4dba-7cea-ac43-c200fdf33788_terseLabel_en-US" xlink:label="lab_bur_InterestRateChangeOf100BpsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate 100bps</link:label>
    <link:label id="lab_bur_InterestRateChangeOf100BpsMember_label_en-US" xlink:label="lab_bur_InterestRateChangeOf100BpsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Change Of 100 bps [Member]</link:label>
    <link:label id="lab_bur_InterestRateChangeOf100BpsMember_documentation_en-US" xlink:label="lab_bur_InterestRateChangeOf100BpsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to change in interest rate of 100bps.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_InterestRateChangeOf100BpsMember" xlink:href="bur-20260630.xsd#bur_InterestRateChangeOf100BpsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_InterestRateChangeOf100BpsMember" xlink:to="lab_bur_InterestRateChangeOf100BpsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FairValueAdjustmentsDomain_019e415a-4e63-7ca5-9311-0f00cd951561_terseLabel_en-US" xlink:label="lab_bur_FairValueAdjustmentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Adjustments [Domain]</link:label>
    <link:label id="lab_bur_FairValueAdjustmentsDomain_label_en-US" xlink:label="lab_bur_FairValueAdjustmentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Adjustments [Domain]</link:label>
    <link:label id="lab_bur_FairValueAdjustmentsDomain_documentation_en-US" xlink:label="lab_bur_FairValueAdjustmentsDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair value adjustment.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FairValueAdjustmentsDomain" xlink:href="bur-20260630.xsd#bur_FairValueAdjustmentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FairValueAdjustmentsDomain" xlink:to="lab_bur_FairValueAdjustmentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFour_019e415a-4e63-7efe-b5b8-f5585099d946_terseLabel_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFour_label_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Rolling Year Four</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFour_documentation_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Rolling Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFour" xlink:href="bur-20260630.xsd#bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFour" xlink:to="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019e415a-4e63-7f52-95d0-7bd2c8c6da9b_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ordinary shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019e415a-4e63-7c7e-a17d-f767eb1e9735_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Ordinary shares, beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019e415a-4e63-7cd7-8e44-e8d71a92c6ba_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ordinary shares, ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019e415a-4e63-7654-a7e9-18068a7961ed_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019e415a-4e63-77c7-9953-881bab8ef94f_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">End of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_019e415a-4e63-79ee-9eea-58d9cdd4b373_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019e415a-4e63-71dc-b950-5950515965c1_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury shares (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019e415a-4e63-7497-8af4-e8dc98fe34e8_negatedPeriodStartLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:type="resource" xml:lang="en-US">Treasury shares, beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019e415a-4e63-749e-8db7-6e74aec8a455_negatedPeriodEndLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:type="resource" xml:lang="en-US">Treasury shares, ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonShares" xlink:to="lab_us-gaap_TreasuryStockCommonShares" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueCurrent_019e415a-4e63-7879-b961-f3a533f51612_verboseLabel_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Current assets</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueCurrent_label_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Held At Fair Value, Current</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueCurrent_documentation_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due from settlement of capital provision assets carrying amounts as of the balance sheet date of all assets that are expected to be realized in cash, sold, or consumed within one year (or the normal operating cycle, if longer).</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccountsReceivableHeldAtFairValueCurrent" xlink:href="bur-20260630.xsd#bur_AccountsReceivableHeldAtFairValueCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccountsReceivableHeldAtFairValueCurrent" xlink:to="lab_bur_AccountsReceivableHeldAtFairValueCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_YpfRelatedAssetsMember_019e415a-4dba-7b27-a221-2b52f350cfcd_terseLabel_en-US" xlink:label="lab_bur_YpfRelatedAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">YPF-related assets:</link:label>
    <link:label id="lab_bur_YpfRelatedAssetsMember_label_en-US" xlink:label="lab_bur_YpfRelatedAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">YPF Related Assets [Member]</link:label>
    <link:label id="lab_bur_YpfRelatedAssetsMember_documentation_en-US" xlink:label="lab_bur_YpfRelatedAssetsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to YPF related assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_YpfRelatedAssetsMember" xlink:href="bur-20260630.xsd#bur_YpfRelatedAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_YpfRelatedAssetsMember" xlink:to="lab_bur_YpfRelatedAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationTypes_019e415a-4e63-793b-9cdd-324d791dff3f_terseLabel_en-US" xlink:label="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationTypes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of litigation types</link:label>
    <link:label id="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationTypes_label_en-US" xlink:label="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationTypes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques, Number Of Litigation Types</link:label>
    <link:label id="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationTypes_documentation_en-US" xlink:label="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationTypes" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The number of litigation types inputs considered for measuring fair value of assets and liabilities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationTypes" xlink:href="bur-20260630.xsd#bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationTypes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationTypes" xlink:to="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationTypes" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019e415a-4dba-7d48-8d96-e52d587f064a_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_019e415a-4e63-7fbf-8130-27948e1bbf5d_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_019e415a-4e63-7f86-b8cd-5ef25aaf421d_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_019e415a-4dba-72c4-be3b-d92163e36b46_negatedLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Valuation allowance</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Valuation Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsValuationAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:to="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_019e415a-4e63-752a-ae22-11e307e00c64_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTable" xlink:to="lab_us-gaap_DisaggregationOfRevenueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019e415a-4e63-79da-90e8-2d404c94dbd1_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_BurfordCapitalGlobalFinanceLLCMember_019e415a-4dba-75e5-91a1-4207e4190a55_terseLabel_en-US" xlink:label="lab_bur_BurfordCapitalGlobalFinanceLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Burford Capital Global Finance LLC</link:label>
    <link:label id="lab_bur_BurfordCapitalGlobalFinanceLLCMember_label_en-US" xlink:label="lab_bur_BurfordCapitalGlobalFinanceLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Burford Capital Global Finance LLC [Member]</link:label>
    <link:label id="lab_bur_BurfordCapitalGlobalFinanceLLCMember_documentation_en-US" xlink:label="lab_bur_BurfordCapitalGlobalFinanceLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to Burford Capital Global Finance Plc .</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_BurfordCapitalGlobalFinanceLLCMember" xlink:href="bur-20260630.xsd#bur_BurfordCapitalGlobalFinanceLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_BurfordCapitalGlobalFinanceLLCMember" xlink:to="lab_bur_BurfordCapitalGlobalFinanceLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019e415a-4e63-7dee-8620-f98c19b49a3b_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to non-controlling interests</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_019e415a-4dba-7ca9-a0bc-9c6896586b4d_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable interest entities</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_019e415a-4e64-783e-a522-fd03ac623b67_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liability</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019e415a-4e63-740f-9aa8-9c157c2e7e25_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019e415a-4dba-75cb-8065-b05cb022bf05_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income/(loss) attributable to Burford Capital Limited shareholders</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingNumberOfSharesAuthorizedToBeRepurchased_019e415a-4e63-7a11-bb98-53c7abc71927_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingNumberOfSharesAuthorizedToBeRepurchased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining authorized repurchase amount (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingNumberOfSharesAuthorizedToBeRepurchased_label_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingNumberOfSharesAuthorizedToBeRepurchased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Remaining Authorized, Number of Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchaseProgramRemainingNumberOfSharesAuthorizedToBeRepurchased" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockRepurchaseProgramRemainingNumberOfSharesAuthorizedToBeRepurchased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchaseProgramRemainingNumberOfSharesAuthorizedToBeRepurchased" xlink:to="lab_us-gaap_StockRepurchaseProgramRemainingNumberOfSharesAuthorizedToBeRepurchased" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsAbstract" xlink:to="lab_us-gaap_SubsequentEventsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleList_019e415a-4dba-7954-9e8b-290ebb7d839a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Liability, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleList_label_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liability, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleList" xlink:to="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputConversionRatioMember_019e415a-4dba-721e-8af8-179e8c6fcabb_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputConversionRatioMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion ratio</link:label>
    <link:label id="lab_bur_MeasurementInputConversionRatioMember_label_en-US" xlink:label="lab_bur_MeasurementInputConversionRatioMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Conversion Ratio [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputConversionRatioMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputConversionRatioMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using conversion ratio.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputConversionRatioMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputConversionRatioMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputConversionRatioMember" xlink:to="lab_bur_MeasurementInputConversionRatioMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_LegalRiskDefinitiveUndrawnCommitments_019e415a-4dba-7f37-82e1-c12d49d3478e_terseLabel_en-US" xlink:label="lab_bur_LegalRiskDefinitiveUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal risk (definitive)</link:label>
    <link:label id="lab_bur_LegalRiskDefinitiveUndrawnCommitments_label_en-US" xlink:label="lab_bur_LegalRiskDefinitiveUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Risk Definitive Undrawn Commitments</link:label>
    <link:label id="lab_bur_LegalRiskDefinitiveUndrawnCommitments_documentation_en-US" xlink:label="lab_bur_LegalRiskDefinitiveUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The amount of Legal risk (definitive) undrawn commitments as at the end of the reporting period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_LegalRiskDefinitiveUndrawnCommitments" xlink:href="bur-20260630.xsd#bur_LegalRiskDefinitiveUndrawnCommitments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_LegalRiskDefinitiveUndrawnCommitments" xlink:to="lab_bur_LegalRiskDefinitiveUndrawnCommitments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecurities_019e415a-4dba-7caf-9bcc-53d7ba789f4b_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marketable securities</link:label>
    <link:label id="lab_us-gaap_MarketableSecurities_label_en-US" xlink:label="lab_us-gaap_MarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MarketableSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecurities" xlink:to="lab_us-gaap_MarketableSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019e415a-4dba-740a-bf0c-e34f7b4203b7_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019e415a-4dba-7707-8338-e68f3af68b72_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Loss on debt extinguishment</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Extinguishment of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:to="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetImpairmentCharges_019e415a-4dba-7b62-ac7b-a91f38622f47_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment</link:label>
    <link:label id="lab_us-gaap_OtherAssetImpairmentCharges_label_en-US" xlink:label="lab_us-gaap_OtherAssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Asset Impairment Charges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetImpairmentCharges" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetImpairmentCharges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetImpairmentCharges" xlink:to="lab_us-gaap_OtherAssetImpairmentCharges" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_UnrestrictedSubsidiariesMember_019e415a-4e63-7358-af13-01c554afbcf4_terseLabel_en-US" xlink:label="lab_bur_UnrestrictedSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrestricted Subsidiaries</link:label>
    <link:label id="lab_bur_UnrestrictedSubsidiariesMember_label_en-US" xlink:label="lab_bur_UnrestrictedSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrestricted Subsidiaries [Member]</link:label>
    <link:label id="lab_bur_UnrestrictedSubsidiariesMember_documentation_en-US" xlink:label="lab_bur_UnrestrictedSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to unrestricted subsidiaries.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_UnrestrictedSubsidiariesMember" xlink:href="bur-20260630.xsd#bur_UnrestrictedSubsidiariesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_UnrestrictedSubsidiariesMember" xlink:to="lab_bur_UnrestrictedSubsidiariesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearThree_019e415a-4dba-7be9-b225-a91903b4a159_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments of Principal in Rolling Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInRollingYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_019e415a-4e63-7748-b7ca-052afeb0721f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption price, percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentRedemptionPricePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedBonusesCurrentAndNoncurrent_019e415a-4e63-7557-9a0a-76988ce046cc_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedBonusesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term incentive compensation payable</link:label>
    <link:label id="lab_us-gaap_AccruedBonusesCurrentAndNoncurrent_019e415a-4e63-773f-bba1-bc9d40a66ec5_periodStartLabel_en-US" xlink:label="lab_us-gaap_AccruedBonusesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning of period</link:label>
    <link:label id="lab_us-gaap_AccruedBonusesCurrentAndNoncurrent_019e415a-4e63-71ba-b217-701d597a929d_periodEndLabel_en-US" xlink:label="lab_us-gaap_AccruedBonusesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">End of period</link:label>
    <link:label id="lab_us-gaap_AccruedBonusesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccruedBonusesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Bonuses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedBonusesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedBonusesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedBonusesCurrentAndNoncurrent" xlink:to="lab_us-gaap_AccruedBonusesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019e415a-4dba-7a2d-ab9d-883ad8e4a6a9_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementCompensationItemsAbstract_019e415a-4dba-7877-a640-5ef7cec0a571_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementCompensationItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation and benefits</link:label>
    <link:label id="lab_us-gaap_IncomeStatementCompensationItemsAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementCompensationItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Items [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementCompensationItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementCompensationItemsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementCompensationItemsAbstract" xlink:to="lab_us-gaap_IncomeStatementCompensationItemsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValue_019e415a-4e63-7d89-9e96-48d645862145_terseLabel_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from settlement of capital provision assets</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValue_019e415a-4e63-7c45-94ab-e01a1ca3a8bd_periodStartLabel_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning of period</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValue_019e415a-4e63-7341-b605-7e3f891012a5_periodEndLabel_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">End of period</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValue_019e415a-4e63-7df7-a6c7-c864505c0733_totalLabel_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total due from settlement of capital provision assets</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValue_label_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Held At Fair Value</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValue_documentation_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Held At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccountsReceivableHeldAtFairValue" xlink:href="bur-20260630.xsd#bur_AccountsReceivableHeldAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccountsReceivableHeldAtFairValue" xlink:to="lab_bur_AccountsReceivableHeldAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_019e415a-4dba-73ce-86aa-eee609e5bd69_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_019e415a-4dba-7c90-b79a-f6204e842bf0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gross deferred tax liabilities</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019e415a-4e63-7525-af2a-587bc998d25b_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019e415a-4e63-771b-af36-bacbd49fd5c5_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BondsMember_019e415a-4dba-79cc-9557-cc936a74dfb9_terseLabel_en-US" xlink:label="lab_us-gaap_BondsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bonds</link:label>
    <link:label id="lab_us-gaap_BondsMember_label_en-US" xlink:label="lab_us-gaap_BondsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bonds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BondsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BondsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BondsMember" xlink:to="lab_us-gaap_BondsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts_019e415a-4e64-7a82-ad89-5640b4b87bac_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Debt extinguishment</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Debt Extinguishment or Debt Prepayment Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDebtExtinguishmentCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:to="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e415a-4dba-76ed-bef5-09592658b74f_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019e415a-4dba-764a-96a5-78043619109e_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies (Note 15)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_019e415a-4dba-7607-a207-b99a0b2f7559_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_019e415a-4dba-7771-99ed-1be9ad8a8dc0_verboseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DiscretionaryUndrawnCommitments_019e415a-4dba-7c10-b862-aa79ac7c0313_terseLabel_en-US" xlink:label="lab_bur_DiscretionaryUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discretionary</link:label>
    <link:label id="lab_bur_DiscretionaryUndrawnCommitments_label_en-US" xlink:label="lab_bur_DiscretionaryUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discretionary Undrawn Commitments</link:label>
    <link:label id="lab_bur_DiscretionaryUndrawnCommitments_documentation_en-US" xlink:label="lab_bur_DiscretionaryUndrawnCommitments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The amount of discretionary undrawn commitments as at the end of the reporting period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DiscretionaryUndrawnCommitments" xlink:href="bur-20260630.xsd#bur_DiscretionaryUndrawnCommitments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DiscretionaryUndrawnCommitments" xlink:to="lab_bur_DiscretionaryUndrawnCommitments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_LaborAndRelatedExpenseReversal_019e415a-4e63-7e98-8505-660fd126c9b0_terseLabel_en-US" xlink:label="lab_bur_LaborAndRelatedExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term incentive compensation including accruals reversal</link:label>
    <link:label id="lab_bur_LaborAndRelatedExpenseReversal_label_en-US" xlink:label="lab_bur_LaborAndRelatedExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Labor and Related Expense Reversal</link:label>
    <link:label id="lab_bur_LaborAndRelatedExpenseReversal_documentation_en-US" xlink:label="lab_bur_LaborAndRelatedExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Labor and Related Expense Reversal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_LaborAndRelatedExpenseReversal" xlink:href="bur-20260630.xsd#bur_LaborAndRelatedExpenseReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_LaborAndRelatedExpenseReversal" xlink:to="lab_bur_LaborAndRelatedExpenseReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsMember_019e415a-4e63-70b3-ab86-aa5d6bb503e5_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Core legal finance (EP Funds)</link:label>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsMember_label_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets Core Legal Finance EP Funds [Member]</link:label>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsMember_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Assets Core Legal Finance EP Funds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsCoreLegalFinanceEPFundsMember" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsCoreLegalFinanceEPFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsCoreLegalFinanceEPFundsMember" xlink:to="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FinancialInstrumentIncreaseInExpectedTimingOfAFavorableOutcome_019e415a-4e63-7c9c-8761-9107d202e4d0_terseLabel_en-US" xlink:label="lab_bur_FinancialInstrumentIncreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in expected timing of a favorable outcome</link:label>
    <link:label id="lab_bur_FinancialInstrumentIncreaseInExpectedTimingOfAFavorableOutcome_label_en-US" xlink:label="lab_bur_FinancialInstrumentIncreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument, Increase In Expected Timing Of A Favorable Outcome</link:label>
    <link:label id="lab_bur_FinancialInstrumentIncreaseInExpectedTimingOfAFavorableOutcome_documentation_en-US" xlink:label="lab_bur_FinancialInstrumentIncreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the increase in expected timing of a favorable outcome.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FinancialInstrumentIncreaseInExpectedTimingOfAFavorableOutcome" xlink:href="bur-20260630.xsd#bur_FinancialInstrumentIncreaseInExpectedTimingOfAFavorableOutcome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FinancialInstrumentIncreaseInExpectedTimingOfAFavorableOutcome" xlink:to="lab_bur_FinancialInstrumentIncreaseInExpectedTimingOfAFavorableOutcome" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ScheduleOfCapitalProvisionUndrawnCommitmentsTableTextBlock_019e415a-4e63-79ef-b696-0c65589d6294_terseLabel_en-US" xlink:label="lab_bur_ScheduleOfCapitalProvisionUndrawnCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Capital Provisions for Undrawn Commitments</link:label>
    <link:label id="lab_bur_ScheduleOfCapitalProvisionUndrawnCommitmentsTableTextBlock_label_en-US" xlink:label="lab_bur_ScheduleOfCapitalProvisionUndrawnCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Capital Provision Undrawn Commitments [Table Text Block]</link:label>
    <link:label id="lab_bur_ScheduleOfCapitalProvisionUndrawnCommitmentsTableTextBlock_documentation_en-US" xlink:label="lab_bur_ScheduleOfCapitalProvisionUndrawnCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tabular disclosure of capital provision undrawn commitments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ScheduleOfCapitalProvisionUndrawnCommitmentsTableTextBlock" xlink:href="bur-20260630.xsd#bur_ScheduleOfCapitalProvisionUndrawnCommitmentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ScheduleOfCapitalProvisionUndrawnCommitmentsTableTextBlock" xlink:to="lab_bur_ScheduleOfCapitalProvisionUndrawnCommitmentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019e415a-4e63-7a10-8c3d-45a21bc70f46_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of assets and liabilities</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_019e415a-4dba-71bc-a2bd-d816a8886ddd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019e415a-4e63-78b1-b1fe-3619b63bada6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_019e415a-4dba-7e72-91af-90712266da55_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosure</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MaximumExposureToCreditRiskOfFinancialAssets_019e415a-4e63-7c3e-8f70-e6175b166d94_terseLabel_en-US" xlink:label="lab_bur_MaximumExposureToCreditRiskOfFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum credit exposure</link:label>
    <link:label id="lab_bur_MaximumExposureToCreditRiskOfFinancialAssets_label_en-US" xlink:label="lab_bur_MaximumExposureToCreditRiskOfFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum Exposure To Credit Risk Of Financial Assets</link:label>
    <link:label id="lab_bur_MaximumExposureToCreditRiskOfFinancialAssets_documentation_en-US" xlink:label="lab_bur_MaximumExposureToCreditRiskOfFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The maximum exposure to the credit risk of financial assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MaximumExposureToCreditRiskOfFinancialAssets" xlink:href="bur-20260630.xsd#bur_MaximumExposureToCreditRiskOfFinancialAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MaximumExposureToCreditRiskOfFinancialAssets" xlink:to="lab_bur_MaximumExposureToCreditRiskOfFinancialAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed_019e415a-4dba-7fe4-aa7c-afa882376b33_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of principal amount to be redeemed</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Percentage of Principal Amount Redeemed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_019e415a-4e63-7be7-8abe-8bc35336cb92_negatedLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Acquisition of ordinary shares held in treasury (shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_label_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares, Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockSharesAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockSharesAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockSharesAcquired" xlink:to="lab_us-gaap_TreasuryStockSharesAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorizedUnlimited_019e415a-4dba-7c47-8e3a-c26d30d2adf4_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorizedUnlimited" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized, Unlimited [Fixed List]</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorizedUnlimited_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorizedUnlimited" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized, Unlimited [Fixed List]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorizedUnlimited" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorizedUnlimited"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorizedUnlimited" xlink:to="lab_us-gaap_CommonStockSharesAuthorizedUnlimited" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_NoCaseMilestoneMember_019e415a-4dba-7446-8f83-16ca7e4bb4a2_terseLabel_en-US" xlink:label="lab_bur_NoCaseMilestoneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">No case milestone:</link:label>
    <link:label id="lab_bur_NoCaseMilestoneMember_label_en-US" xlink:label="lab_bur_NoCaseMilestoneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">No Case Milestone [Member]</link:label>
    <link:label id="lab_bur_NoCaseMilestoneMember_documentation_en-US" xlink:label="lab_bur_NoCaseMilestoneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to no case milestone.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_NoCaseMilestoneMember" xlink:href="bur-20260630.xsd#bur_NoCaseMilestoneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_NoCaseMilestoneMember" xlink:to="lab_bur_NoCaseMilestoneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccountsReceivableCost_019e415a-4e63-780c-87eb-1825453031c3_terseLabel_en-US" xlink:label="lab_bur_AccountsReceivableCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from settlement of capital provision assets, Cost</link:label>
    <link:label id="lab_bur_AccountsReceivableCost_label_en-US" xlink:label="lab_bur_AccountsReceivableCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Cost</link:label>
    <link:label id="lab_bur_AccountsReceivableCost_documentation_en-US" xlink:label="lab_bur_AccountsReceivableCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccountsReceivableCost" xlink:href="bur-20260630.xsd#bur_AccountsReceivableCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccountsReceivableCost" xlink:to="lab_bur_AccountsReceivableCost" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsSingleMember_019e415a-4dba-7251-9121-ce083db80b0b_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsSingleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Single case</link:label>
    <link:label id="lab_bur_DerivativeAssetsSingleMember_label_en-US" xlink:label="lab_bur_DerivativeAssetsSingleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets, Single [Member]</link:label>
    <link:label id="lab_bur_DerivativeAssetsSingleMember_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsSingleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to capital provision assets single.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsSingleMember" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsSingleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsSingleMember" xlink:to="lab_bur_DerivativeAssetsSingleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_019e415a-4dba-7c3f-8219-dded07c4fc9c_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Cash paid for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, before Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxesPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaid" xlink:to="lab_us-gaap_IncomeTaxesPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_A12MonthsDurationMember_019e415a-4dba-7204-a2f2-2587318b305f_terseLabel_en-US" xlink:label="lab_bur_A12MonthsDurationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">12 months duration</link:label>
    <link:label id="lab_bur_A12MonthsDurationMember_label_en-US" xlink:label="lab_bur_A12MonthsDurationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">12 Months Duration [Member]</link:label>
    <link:label id="lab_bur_A12MonthsDurationMember_documentation_en-US" xlink:label="lab_bur_A12MonthsDurationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the member information pertaining to expected timing of a favorable outcome of twelve months.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_A12MonthsDurationMember" xlink:href="bur-20260630.xsd#bur_A12MonthsDurationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_A12MonthsDurationMember" xlink:to="lab_bur_A12MonthsDurationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_019e415a-4dba-7b86-af96-ee21b1bcfbd8_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019e415a-4dba-7789-80ca-8b370911b7ee_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsTransfersBetweenLevels_019e415a-4e63-7211-9726-2f41b2b4b047_terseLabel_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsTransfersBetweenLevels" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers</link:label>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsTransfersBetweenLevels_label_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsTransfersBetweenLevels" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Assets Transfers Between Levels</link:label>
    <link:label id="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsTransfersBetweenLevels_documentation_en-US" xlink:label="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsTransfersBetweenLevels" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of transfer of financial instrument classified as an asset into level 3 of the fair value hierarchy.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsTransfersBetweenLevels" xlink:href="bur-20260630.xsd#bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsTransfersBetweenLevels"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsTransfersBetweenLevels" xlink:to="lab_bur_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetsTransfersBetweenLevels" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_019e415a-4e63-7429-a47e-6a68dcce2a8a_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MutualFundMember_019e415a-4e63-7533-addd-236da394c8d3_terseLabel_en-US" xlink:label="lab_us-gaap_MutualFundMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mutual funds</link:label>
    <link:label id="lab_us-gaap_MutualFundMember_label_en-US" xlink:label="lab_us-gaap_MutualFundMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mutual Fund [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MutualFundMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MutualFundMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MutualFundMember" xlink:to="lab_us-gaap_MutualFundMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_019e415a-4dba-7394-8ca0-3b973ed5fa7f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Acquisition of ordinary shares held in treasury</link:label>
    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_label_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Value, Acquired, Cost Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockValueAcquiredCostMethod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:to="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e415a-4dba-7121-a54c-4432efb0df8e_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents at beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e415a-4dba-769b-9228-8177e3dafb4d_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents at end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_PaymentsForVariableInterestEntities_019e415a-4e63-7aef-a2a9-4ff0024eab59_negatedLabel_en-US" xlink:label="lab_bur_PaymentsForVariableInterestEntities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">(Funding)</link:label>
    <link:label id="lab_bur_PaymentsForVariableInterestEntities_label_en-US" xlink:label="lab_bur_PaymentsForVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For Variable Interest Entities</link:label>
    <link:label id="lab_bur_PaymentsForVariableInterestEntities_documentation_en-US" xlink:label="lab_bur_PaymentsForVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The net cash outflow from VIEs.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_PaymentsForVariableInterestEntities" xlink:href="bur-20260630.xsd#bur_PaymentsForVariableInterestEntities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_PaymentsForVariableInterestEntities" xlink:to="lab_bur_PaymentsForVariableInterestEntities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019e415a-4e63-7d8c-ac09-e1620b92b5a4_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ThirdPartyInterestInCapitalProvisionAssetsPolicyTextBlock_019e415a-4dba-7af7-b1a0-29cbd29c56eb_terseLabel_en-US" xlink:label="lab_bur_ThirdPartyInterestInCapitalProvisionAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Third-party interests in capital provision assets</link:label>
    <link:label id="lab_bur_ThirdPartyInterestInCapitalProvisionAssetsPolicyTextBlock_label_en-US" xlink:label="lab_bur_ThirdPartyInterestInCapitalProvisionAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third Party Interest In Capital Provision Assets [Policy Text Block]</link:label>
    <link:label id="lab_bur_ThirdPartyInterestInCapitalProvisionAssetsPolicyTextBlock_documentation_en-US" xlink:label="lab_bur_ThirdPartyInterestInCapitalProvisionAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disclosure of accounting policy for third party interest in capital provision assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ThirdPartyInterestInCapitalProvisionAssetsPolicyTextBlock" xlink:href="bur-20260630.xsd#bur_ThirdPartyInterestInCapitalProvisionAssetsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ThirdPartyInterestInCapitalProvisionAssetsPolicyTextBlock" xlink:to="lab_bur_ThirdPartyInterestInCapitalProvisionAssetsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases_019e415a-4dba-7bfe-b973-dfd96e4d58d0_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deployments</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:to="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFive_019e415a-4e63-7dc1-bf24-02d72fff170a_terseLabel_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFive_label_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Rolling Year Five</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFive_documentation_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Rolling Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFive" xlink:href="bur-20260630.xsd#bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFive" xlink:to="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_019e415a-4e64-789e-a563-6635cca7cb56_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e415a-4dba-71cf-9ec4-b0743f186180_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income/(loss)</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019e415a-4e63-740c-9dd3-faa089165d96_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueOtherIncome_019e415a-4e63-7ccf-981b-cef29a8b6cb3_terseLabel_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueOtherIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss)</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueOtherIncome_label_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueOtherIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Held At Fair Value, Other Income</link:label>
    <link:label id="lab_bur_AccountsReceivableHeldAtFairValueOtherIncome_documentation_en-US" xlink:label="lab_bur_AccountsReceivableHeldAtFairValueOtherIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of other income on financial asset recognized at fair value through profit or loss.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccountsReceivableHeldAtFairValueOtherIncome" xlink:href="bur-20260630.xsd#bur_AccountsReceivableHeldAtFairValueOtherIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccountsReceivableHeldAtFairValueOtherIncome" xlink:to="lab_bur_AccountsReceivableHeldAtFairValueOtherIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_019e415a-4e63-7abf-af32-8fe04264c961_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based and deferred compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_019e415a-4dba-7039-8b05-f9f096c01852_terseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term incentive compensation including accruals</link:label>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_label_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Labor and Related Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LaborAndRelatedExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LaborAndRelatedExpense" xlink:to="lab_us-gaap_LaborAndRelatedExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019e415a-4dba-7cfc-9088-492b19b67239_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019e415a-4e63-786f-b44d-ba5ee3af2bc6_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_019e415a-4e63-7de5-bcd1-4f4f9198aa24_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_019e415a-4dba-77f0-bad5-cd7c363ea4d2_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Acquisition of ordinary shares held in treasury</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019e415a-4dba-74ca-964e-801e195f132c_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019e415a-4e63-7dc7-9603-ba33810412d4_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_019e415a-4dba-70f9-b7d9-e432d7c508b2_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019e415a-4dba-7032-a557-180d1d8122c7_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ordinary shares</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputPortfoliosWithMultipleFactorsMember_019e415a-4dba-7ccf-8c95-0464d88bb09e_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputPortfoliosWithMultipleFactorsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portfolios with multiple factors</link:label>
    <link:label id="lab_bur_MeasurementInputPortfoliosWithMultipleFactorsMember_label_en-US" xlink:label="lab_bur_MeasurementInputPortfoliosWithMultipleFactorsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Portfolios With Multiple Factors [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputPortfoliosWithMultipleFactorsMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputPortfoliosWithMultipleFactorsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using portfolios with multiple factors.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputPortfoliosWithMultipleFactorsMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputPortfoliosWithMultipleFactorsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputPortfoliosWithMultipleFactorsMember" xlink:to="lab_bur_MeasurementInputPortfoliosWithMultipleFactorsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_UnrealizedFairValueDerivativeAssets_019e415a-4dba-7486-ab3c-9b0726434bc8_verboseLabel_en-US" xlink:label="lab_bur_UnrealizedFairValueDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unrealized fair value, end of period</link:label>
    <link:label id="lab_bur_UnrealizedFairValueDerivativeAssets_label_en-US" xlink:label="lab_bur_UnrealizedFairValueDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Fair Value, Derivative Assets</link:label>
    <link:label id="lab_bur_UnrealizedFairValueDerivativeAssets_documentation_en-US" xlink:label="lab_bur_UnrealizedFairValueDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrealized fair value of capital provision assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_UnrealizedFairValueDerivativeAssets" xlink:href="bur-20260630.xsd#bur_UnrealizedFairValueDerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_UnrealizedFairValueDerivativeAssets" xlink:to="lab_bur_UnrealizedFairValueDerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsRollForwardRollForward_019e415a-4dba-7e80-a6fc-2248bc9e90a3_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsRollForwardRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Assets [Roll Forward]</link:label>
    <link:label id="lab_bur_DerivativeAssetsRollForwardRollForward_label_en-US" xlink:label="lab_bur_DerivativeAssetsRollForwardRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets Roll Forward [Roll Forward]</link:label>
    <link:label id="lab_bur_DerivativeAssetsRollForwardRollForward_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsRollForwardRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Assets Roll Forward</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsRollForwardRollForward" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsRollForwardRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsRollForwardRollForward" xlink:to="lab_bur_DerivativeAssetsRollForwardRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ProceedsFromVariableInterestEntities_019e415a-4dba-7bfc-af78-c71fe56b59f4_terseLabel_en-US" xlink:label="lab_bur_ProceedsFromVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds</link:label>
    <link:label id="lab_bur_ProceedsFromVariableInterestEntities_label_en-US" xlink:label="lab_bur_ProceedsFromVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Variable Interest Entities</link:label>
    <link:label id="lab_bur_ProceedsFromVariableInterestEntities_documentation_en-US" xlink:label="lab_bur_ProceedsFromVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The net cash inflow from VIEs.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ProceedsFromVariableInterestEntities" xlink:href="bur-20260630.xsd#bur_ProceedsFromVariableInterestEntities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ProceedsFromVariableInterestEntities" xlink:to="lab_bur_ProceedsFromVariableInterestEntities" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_UnsecuredNotes8.50PercentDueJanuary2034Member_019e415a-4e63-7f38-9aea-6d95ed456505_terseLabel_en-US" xlink:label="lab_bur_UnsecuredNotes8.50PercentDueJanuary2034Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">8.50% Senior Notes due January 15, 2034</link:label>
    <link:label id="lab_bur_UnsecuredNotes8.50PercentDueJanuary2034Member_label_en-US" xlink:label="lab_bur_UnsecuredNotes8.50PercentDueJanuary2034Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Notes 8.50 Percent Due January 2034 [Member]</link:label>
    <link:label id="lab_bur_UnsecuredNotes8.50PercentDueJanuary2034Member_documentation_en-US" xlink:label="lab_bur_UnsecuredNotes8.50PercentDueJanuary2034Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Notes 8.50 Percent Due January 2034</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_UnsecuredNotes8.50PercentDueJanuary2034Member" xlink:href="bur-20260630.xsd#bur_UnsecuredNotes8.50PercentDueJanuary2034Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_UnsecuredNotes8.50PercentDueJanuary2034Member" xlink:to="lab_bur_UnsecuredNotes8.50PercentDueJanuary2034Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFinancialInstrumentsAssetsMember_019e415a-4dba-777d-b3e2-31682e167043_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFinancialInstrumentsAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital provision assets</link:label>
    <link:label id="lab_us-gaap_DerivativeFinancialInstrumentsAssetsMember_label_en-US" xlink:label="lab_us-gaap_DerivativeFinancialInstrumentsAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Financial Instruments, Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFinancialInstrumentsAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFinancialInstrumentsAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFinancialInstrumentsAssetsMember" xlink:to="lab_us-gaap_DerivativeFinancialInstrumentsAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019e415a-4e63-7915-901c-18c8afdc56cb_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities and shareholders' equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MarketableSecurityGainLossAndInterestIncome_019e415a-4e63-7cd1-842f-25b5951e46d5_terseLabel_en-US" xlink:label="lab_bur_MarketableSecurityGainLossAndInterestIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marketable securities income/(loss) and interest</link:label>
    <link:label id="lab_bur_MarketableSecurityGainLossAndInterestIncome_label_en-US" xlink:label="lab_bur_MarketableSecurityGainLossAndInterestIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Security, Gain (Loss) And Interest Income</link:label>
    <link:label id="lab_bur_MarketableSecurityGainLossAndInterestIncome_documentation_en-US" xlink:label="lab_bur_MarketableSecurityGainLossAndInterestIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marketable Security, Gain (Loss) And Interest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MarketableSecurityGainLossAndInterestIncome" xlink:href="bur-20260630.xsd#bur_MarketableSecurityGainLossAndInterestIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MarketableSecurityGainLossAndInterestIncome" xlink:to="lab_bur_MarketableSecurityGainLossAndInterestIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealizedInvestmentGainsLosses_019e415a-4e63-7586-a1a1-8b81bdb6f803_terseLabel_en-US" xlink:label="lab_us-gaap_RealizedInvestmentGainsLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized gains/(losses)</link:label>
    <link:label id="lab_us-gaap_RealizedInvestmentGainsLosses_label_en-US" xlink:label="lab_us-gaap_RealizedInvestmentGainsLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Investment Gains (Losses)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealizedInvestmentGainsLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealizedInvestmentGainsLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealizedInvestmentGainsLosses" xlink:to="lab_us-gaap_RealizedInvestmentGainsLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_019e415a-4dba-7283-90a6-de02c0afd0d1_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deployments</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_019e415a-4e63-7154-9302-35112dc52f8f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_019e415a-4dba-7ec3-97e5-80db2a59c00f_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-controlling interests</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019e415a-4e63-72e7-83c5-975f5b75663b_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_019e415a-4e63-7fdb-a49c-5690c712eebd_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase/(decrease) in other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ChangeInInterestRateAxis_019e415a-4dba-7dd7-b648-07690418fc0b_terseLabel_en-US" xlink:label="lab_bur_ChangeInInterestRateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change In Interest Rate [Axis]</link:label>
    <link:label id="lab_bur_ChangeInInterestRateAxis_label_en-US" xlink:label="lab_bur_ChangeInInterestRateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change In Interest Rate [Axis]</link:label>
    <link:label id="lab_bur_ChangeInInterestRateAxis_documentation_en-US" xlink:label="lab_bur_ChangeInInterestRateAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Change In Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ChangeInInterestRateAxis" xlink:href="bur-20260630.xsd#bur_ChangeInInterestRateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ChangeInInterestRateAxis" xlink:to="lab_bur_ChangeInInterestRateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019e415a-4e63-7366-b955-15452b299ee8_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_019e415a-4e63-7e22-b20e-6ce9b5424aef_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Due From Settlement of Capital Provision Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019e415a-4e63-7d8f-9f6e-223d91928d56_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ExpenditureIneligibleForInclusionInAssetCost_019e415a-4dba-7fd0-a83c-49c5a2af3f4e_verboseLabel_en-US" xlink:label="lab_bur_ExpenditureIneligibleForInclusionInAssetCost" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Case-related expenditures ineligible for inclusion in asset cost</link:label>
    <link:label id="lab_bur_ExpenditureIneligibleForInclusionInAssetCost_label_en-US" xlink:label="lab_bur_ExpenditureIneligibleForInclusionInAssetCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Expenditure Ineligible For Inclusion In Asset Cost</link:label>
    <link:label id="lab_bur_ExpenditureIneligibleForInclusionInAssetCost_documentation_en-US" xlink:label="lab_bur_ExpenditureIneligibleForInclusionInAssetCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The amount of case-related expenditure that are ineligible for inclusion in asset cost.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ExpenditureIneligibleForInclusionInAssetCost" xlink:href="bur-20260630.xsd#bur_ExpenditureIneligibleForInclusionInAssetCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ExpenditureIneligibleForInclusionInAssetCost" xlink:to="lab_bur_ExpenditureIneligibleForInclusionInAssetCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ParentMember_019e415a-4e63-7d9f-a99d-df4f99703b21_terseLabel_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Burford Capital Limited equity</link:label>
    <link:label id="lab_us-gaap_ParentMember_label_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ParentMember" xlink:to="lab_us-gaap_ParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DebtInstrumentRedemptionMinimumPrincipalAmountOutstandingAsAPercentage_019e415a-4e63-7ccf-92f8-6de9d7190757_terseLabel_en-US" xlink:label="lab_bur_DebtInstrumentRedemptionMinimumPrincipalAmountOutstandingAsAPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum principal amount outstanding, percentage</link:label>
    <link:label id="lab_bur_DebtInstrumentRedemptionMinimumPrincipalAmountOutstandingAsAPercentage_label_en-US" xlink:label="lab_bur_DebtInstrumentRedemptionMinimumPrincipalAmountOutstandingAsAPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Minimum Principal Amount Outstanding, As A Percentage</link:label>
    <link:label id="lab_bur_DebtInstrumentRedemptionMinimumPrincipalAmountOutstandingAsAPercentage_documentation_en-US" xlink:label="lab_bur_DebtInstrumentRedemptionMinimumPrincipalAmountOutstandingAsAPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Minimum Principal Amount Outstanding, As A Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DebtInstrumentRedemptionMinimumPrincipalAmountOutstandingAsAPercentage" xlink:href="bur-20260630.xsd#bur_DebtInstrumentRedemptionMinimumPrincipalAmountOutstandingAsAPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DebtInstrumentRedemptionMinimumPrincipalAmountOutstandingAsAPercentage" xlink:to="lab_bur_DebtInstrumentRedemptionMinimumPrincipalAmountOutstandingAsAPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsUnrealizedGainLoss_019e415a-4dba-73cf-b2d7-44420efbc6e0_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital provision assets, Unrealized</link:label>
    <link:label id="lab_bur_DerivativeAssetsUnrealizedGainLoss_label_en-US" xlink:label="lab_bur_DerivativeAssetsUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_bur_DerivativeAssetsUnrealizedGainLoss_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of unrealized gain (loss) on capital provision assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsUnrealizedGainLoss" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsUnrealizedGainLoss" xlink:to="lab_bur_DerivativeAssetsUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_019e415a-4dba-7afc-bf5a-381550af4098_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shareholders' equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCountry_019e415a-4e63-70c7-aac3-4a315da3e1cb_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCountry" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Country</link:label>
    <link:label id="lab_dei_EntityAddressCountry_label_en-US" xlink:label="lab_dei_EntityAddressCountry" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Country</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCountry"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCountry" xlink:to="lab_dei_EntityAddressCountry" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:to="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_CorporateBondsMember_019e415a-4dba-775d-95f5-2d0068ec0ee8_terseLabel_en-US" xlink:label="lab_bur_CorporateBondsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate bonds</link:label>
    <link:label id="lab_bur_CorporateBondsMember_label_en-US" xlink:label="lab_bur_CorporateBondsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Bonds [Member]</link:label>
    <link:label id="lab_bur_CorporateBondsMember_documentation_en-US" xlink:label="lab_bur_CorporateBondsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to corporate bonds.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_CorporateBondsMember" xlink:href="bur-20260630.xsd#bur_CorporateBondsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_CorporateBondsMember" xlink:to="lab_bur_CorporateBondsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_019e415a-4dba-7e3e-a782-56cec45b129b_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General, administrative and other</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_MeasurementInputSettlementMember_019e415a-4e63-7b3f-92ac-659901a446b0_terseLabel_en-US" xlink:label="lab_bur_MeasurementInputSettlementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Settlement</link:label>
    <link:label id="lab_bur_MeasurementInputSettlementMember_label_en-US" xlink:label="lab_bur_MeasurementInputSettlementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Settlement [Member]</link:label>
    <link:label id="lab_bur_MeasurementInputSettlementMember_documentation_en-US" xlink:label="lab_bur_MeasurementInputSettlementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement input using settlement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_MeasurementInputSettlementMember" xlink:href="bur-20260630.xsd#bur_MeasurementInputSettlementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_MeasurementInputSettlementMember" xlink:to="lab_bur_MeasurementInputSettlementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesCost_019e415a-4e63-7c68-a769-5d01c99c8c18_terseLabel_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets of consolidated investment companies, Cost</link:label>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesCost_label_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Of Consolidated Investment Companies, Cost</link:label>
    <link:label id="lab_bur_AssetsOfConsolidatedInvestmentCompaniesCost_documentation_en-US" xlink:label="lab_bur_AssetsOfConsolidatedInvestmentCompaniesCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets Of Consolidated Investment Companies, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AssetsOfConsolidatedInvestmentCompaniesCost" xlink:href="bur-20260630.xsd#bur_AssetsOfConsolidatedInvestmentCompaniesCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AssetsOfConsolidatedInvestmentCompaniesCost" xlink:to="lab_bur_AssetsOfConsolidatedInvestmentCompaniesCost" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_ThirdPartyInterestsInCapitalProvisionAssetsMember_019e415a-4e63-7b6d-907b-9b1ea23ae685_terseLabel_en-US" xlink:label="lab_bur_ThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plus/(Less): Third-party interests in capital provision assets</link:label>
    <link:label id="lab_bur_ThirdPartyInterestsInCapitalProvisionAssetsMember_label_en-US" xlink:label="lab_bur_ThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third Party Interests In Capital Provision Assets [Member]</link:label>
    <link:label id="lab_bur_ThirdPartyInterestsInCapitalProvisionAssetsMember_documentation_en-US" xlink:label="lab_bur_ThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Third Party Interests In Capital Provision Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_ThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:href="bur-20260630.xsd#bur_ThirdPartyInterestsInCapitalProvisionAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_ThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:to="lab_bur_ThirdPartyInterestsInCapitalProvisionAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_019e415a-4e63-752e-92b4-f25437e7dcc4_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial liabilities relating to third-party interests in capital provision assets</link:label>
    <link:label id="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_label_en-US" xlink:label="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Financial Instruments, Liabilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:to="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditConcentrationRiskMember_019e415a-4dba-72fa-b888-17079053589d_terseLabel_en-US" xlink:label="lab_us-gaap_CreditConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Concentration Risk</link:label>
    <link:label id="lab_us-gaap_CreditConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_CreditConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditConcentrationRiskMember" xlink:to="lab_us-gaap_CreditConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_019e415a-4dba-7e57-8cf0-8cbbd959eca1_negatedLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Cash paid for debt interest</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySales_019e415a-4dba-76f2-82e2-415c158c57ed_negatedLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySales" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Realizations</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySales_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySales" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySales" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySales"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySales" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySales" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInExpectedTimingOfAFavorableOutcome_019e415a-4dba-78f6-b89f-6ef6d80d2192_negatedLabel_en-US" xlink:label="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Decrease in consolidated income and net assets due to increase in expected timing of a favorable outcome</link:label>
    <link:label id="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInExpectedTimingOfAFavorableOutcome_label_en-US" xlink:label="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Decrease In Consolidated Income And Net Assets Due To Increase In Expected Timing Of A Favorable Outcome</link:label>
    <link:label id="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInExpectedTimingOfAFavorableOutcome_documentation_en-US" xlink:label="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of decrease in consolidated income and net assets due to increase in expected timing of a favorable outcome.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInExpectedTimingOfAFavorableOutcome" xlink:href="bur-20260630.xsd#bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInExpectedTimingOfAFavorableOutcome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInExpectedTimingOfAFavorableOutcome" xlink:to="lab_bur_DecreaseInConsolidatedIncomeAndNetAssetsDueToIncreaseInExpectedTimingOfAFavorableOutcome" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019e415a-4dba-7d0d-8593-14f7cd083055_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
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    <link:label id="lab_bur_IncreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseInExpectedTimingOfAFavorableOutcome_label_en-US" xlink:label="lab_bur_IncreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase In Consolidated Income And Net Assets Due To Decrease In Expected Timing Of A Favorable Outcome</link:label>
    <link:label id="lab_bur_IncreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseInExpectedTimingOfAFavorableOutcome_documentation_en-US" xlink:label="lab_bur_IncreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseInExpectedTimingOfAFavorableOutcome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of increase in consolidated income and net assets due to decrease in expected timing of a favorable outcome.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_IncreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseInExpectedTimingOfAFavorableOutcome" xlink:href="bur-20260630.xsd#bur_IncreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseInExpectedTimingOfAFavorableOutcome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_IncreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseInExpectedTimingOfAFavorableOutcome" xlink:to="lab_bur_IncreaseInConsolidatedIncomeAndNetAssetsDueToDecreaseInExpectedTimingOfAFavorableOutcome" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_019e415a-4e63-78e7-b072-970b3e70a7ed_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019e415a-4dba-7ec2-9ff3-50ce34d4396f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_019e415a-4dba-7981-bb78-a09dbf8aa6fc_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_BurfordCapitalPlcMember_019e415a-4e64-74ce-a7b9-37d6fec912d5_terseLabel_en-US" xlink:label="lab_bur_BurfordCapitalPlcMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Burford Capital PLC</link:label>
    <link:label id="lab_bur_BurfordCapitalPlcMember_label_en-US" xlink:label="lab_bur_BurfordCapitalPlcMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Burford Capital Plc [Member]</link:label>
    <link:label id="lab_bur_BurfordCapitalPlcMember_documentation_en-US" xlink:label="lab_bur_BurfordCapitalPlcMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to Burford Capital Plc.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_BurfordCapitalPlcMember" xlink:href="bur-20260630.xsd#bur_BurfordCapitalPlcMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_BurfordCapitalPlcMember" xlink:to="lab_bur_BurfordCapitalPlcMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019e415a-4e63-7fbe-ad4b-51680d62f03c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_NetRealizedAndUnrealizedGainLossOnAccountsReceivable_019e415a-4dba-7261-889e-daf4f25aa892_terseLabel_en-US" xlink:label="lab_bur_NetRealizedAndUnrealizedGainLossOnAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) from due from settlement of capital provision assets</link:label>
    <link:label id="lab_bur_NetRealizedAndUnrealizedGainLossOnAccountsReceivable_label_en-US" xlink:label="lab_bur_NetRealizedAndUnrealizedGainLossOnAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Realized And Unrealized Gain (Loss) On Accounts Receivable</link:label>
    <link:label id="lab_bur_NetRealizedAndUnrealizedGainLossOnAccountsReceivable_documentation_en-US" xlink:label="lab_bur_NetRealizedAndUnrealizedGainLossOnAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of net realized and unrealized gain (loss) on due from settlement of capital provision assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_NetRealizedAndUnrealizedGainLossOnAccountsReceivable" xlink:href="bur-20260630.xsd#bur_NetRealizedAndUnrealizedGainLossOnAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_NetRealizedAndUnrealizedGainLossOnAccountsReceivable" xlink:to="lab_bur_NetRealizedAndUnrealizedGainLossOnAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_019e415a-4dba-743f-9bb1-79f6bf008e3c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Capital Provision Income on Consolidated Statement of Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivatives Instruments Statements of Financial Performance and Financial Position, Location [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_NoncontrollingInterestDecreaseFromDistributionsToNoncontrollingInterestHoldersNetOfContributions_019faaa8-46b5-72f5-8701-33af6b1a9e81_negatedLabel_en-US" xlink:label="lab_bur_NoncontrollingInterestDecreaseFromDistributionsToNoncontrollingInterestHoldersNetOfContributions" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Third-party net capital contribution/(distribution)</link:label>
    <link:label id="lab_bur_NoncontrollingInterestDecreaseFromDistributionsToNoncontrollingInterestHoldersNetOfContributions_label_en-US" xlink:label="lab_bur_NoncontrollingInterestDecreaseFromDistributionsToNoncontrollingInterestHoldersNetOfContributions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders, Net Of Contributions</link:label>
    <link:label id="lab_bur_NoncontrollingInterestDecreaseFromDistributionsToNoncontrollingInterestHoldersNetOfContributions_documentation_en-US" xlink:label="lab_bur_NoncontrollingInterestDecreaseFromDistributionsToNoncontrollingInterestHoldersNetOfContributions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders, Net Of Contributions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_NoncontrollingInterestDecreaseFromDistributionsToNoncontrollingInterestHoldersNetOfContributions" xlink:href="bur-20260630.xsd#bur_NoncontrollingInterestDecreaseFromDistributionsToNoncontrollingInterestHoldersNetOfContributions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_NoncontrollingInterestDecreaseFromDistributionsToNoncontrollingInterestHoldersNetOfContributions" xlink:to="lab_bur_NoncontrollingInterestDecreaseFromDistributionsToNoncontrollingInterestHoldersNetOfContributions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019e415a-4dba-7507-9e3d-61936269bcb9_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019e415a-4dba-7378-a137-7bc16dce882a_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearTwo_019e415a-4dba-7551-bd1b-521bff723184_terseLabel_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearTwo_label_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Rolling Year Two</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearTwo_documentation_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Rolling Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearTwo" xlink:href="bur-20260630.xsd#bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearTwo" xlink:to="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInRollingYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_CompensationAndBenefits_019e415a-4dba-7f3e-8034-e0f9c5bea348_terseLabel_en-US" xlink:label="lab_bur_CompensationAndBenefits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation and benefits</link:label>
    <link:label id="lab_bur_CompensationAndBenefits_label_en-US" xlink:label="lab_bur_CompensationAndBenefits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation And Benefits</link:label>
    <link:label id="lab_bur_CompensationAndBenefits_documentation_en-US" xlink:label="lab_bur_CompensationAndBenefits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Compensation And Benefits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_CompensationAndBenefits" xlink:href="bur-20260630.xsd#bur_CompensationAndBenefits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_CompensationAndBenefits" xlink:to="lab_bur_CompensationAndBenefits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e415a-4e63-7720-a6ab-f02e0639ff63_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e415a-4e63-7a03-a343-b06bb45508e0_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash balance as of end of period</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_019e415a-4dba-7999-a4da-b9a9f7a0d424_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Duration (years)</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Term [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputExpectedTermMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:to="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_019e415a-4dba-77f1-b369-f77d1a03c666_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_019e415a-4dba-76bf-b09e-3f1fe670bda9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Capital provision (income)/loss</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_019e415a-4dba-7dee-9f61-0a4335087f0d_totalLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total capital provision income/(loss) as reported in the unaudited condensed consolidated statements of operations</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments, Net, Pretax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnDerivativeInstrumentsNetPretax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:to="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_019e415a-4dba-77b3-8f34-795e7241c440_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine2" xlink:to="lab_dei_EntityAddressAddressLine2" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList_019e415a-4dba-705c-beec-f15e2322d081_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList_label_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:to="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_019e415a-4dba-7375-a33c-44b7b723e4b2_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of new ordinary shares to satisfy distributions under the NQDC Plan (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_019e415a-4dba-7000-ac7b-2ba30b9dcd99_totalLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_019e415a-4dba-78f1-ae1f-5bcdee94126e_verboseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_019e415a-4dba-7f4c-8ab9-f87d4249aed0_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyExchangeRateTranslation1_019e415a-4dba-7158-8b45-caad20d4d5e5_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange rate</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyExchangeRateTranslation1_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Currency Exchange Rate, Translation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyExchangeRateTranslation1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:to="lab_us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019e415a-4e63-78d2-ae26-7c995ae0f5f9_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial liabilities relating to third-party interests in capital provision assets</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeniorNotesMember_019e415a-4dba-7635-b174-8e39bfd77de3_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes</link:label>
    <link:label id="lab_us-gaap_SeniorNotesMember_label_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorNotesMember" xlink:to="lab_us-gaap_SeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019e415a-4dba-7572-98e7-6ae625fa7280_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_NegativeFairValueAdjustmentsMember_019e415a-4dba-7843-a50f-a61970339b14_terseLabel_en-US" xlink:label="lab_bur_NegativeFairValueAdjustmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Negative case milestone factor:</link:label>
    <link:label id="lab_bur_NegativeFairValueAdjustmentsMember_label_en-US" xlink:label="lab_bur_NegativeFairValueAdjustmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Negative Fair Value Adjustments [Member]</link:label>
    <link:label id="lab_bur_NegativeFairValueAdjustmentsMember_documentation_en-US" xlink:label="lab_bur_NegativeFairValueAdjustmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to negative fair value adjustments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_NegativeFairValueAdjustmentsMember" xlink:href="bur-20260630.xsd#bur_NegativeFairValueAdjustmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_NegativeFairValueAdjustmentsMember" xlink:to="lab_bur_NegativeFairValueAdjustmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019e415a-4dba-72e4-a45f-cbd221c1641d_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Provision for/(benefit from) income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_019e415a-4e63-76c5-8e52-4fb0096f12fb_negatedLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Foreign currency transactions (gains)/losses and other expenses</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_019e415a-4e63-7ed2-8d3f-25b988ddbeef_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange gains/(losses)</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss), Foreign Currency Transaction, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionGainLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:to="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_UnsecuredNotes6.875PercentDueApril2030Member_019e415a-4e63-73ca-869f-2649eecde3a5_terseLabel_en-US" xlink:label="lab_bur_UnsecuredNotes6.875PercentDueApril2030Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">6.875% Senior Notes due 2030</link:label>
    <link:label id="lab_bur_UnsecuredNotes6.875PercentDueApril2030Member_019e415a-4e63-72ee-870d-ad7814bd7cc7_verboseLabel_en-US" xlink:label="lab_bur_UnsecuredNotes6.875PercentDueApril2030Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">6.875% Senior Notes due 2030</link:label>
    <link:label id="lab_bur_UnsecuredNotes6.875PercentDueApril2030Member_label_en-US" xlink:label="lab_bur_UnsecuredNotes6.875PercentDueApril2030Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Notes 6.875 Percent Due April 2030 [Member]</link:label>
    <link:label id="lab_bur_UnsecuredNotes6.875PercentDueApril2030Member_documentation_en-US" xlink:label="lab_bur_UnsecuredNotes6.875PercentDueApril2030Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents information relating to unsecured Notes 6.875 Percent Due April 2030.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_UnsecuredNotes6.875PercentDueApril2030Member" xlink:href="bur-20260630.xsd#bur_UnsecuredNotes6.875PercentDueApril2030Member"/>
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    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMethodTextBlock"/>
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    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019e415a-4e63-78d9-8ac5-4cd8345b080d_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsOtherAdditionsMember_019e415a-4e63-7513-af87-e302c133b839_terseLabel_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsOtherAdditionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Core legal finance (EP Funds), other additions</link:label>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsOtherAdditionsMember_label_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsOtherAdditionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets Core Legal Finance EP Funds, Other Additions [Member]</link:label>
    <link:label id="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsOtherAdditionsMember_documentation_en-US" xlink:label="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsOtherAdditionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Assets Core Legal Finance EP Funds, Other Additions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_DerivativeAssetsCoreLegalFinanceEPFundsOtherAdditionsMember" xlink:href="bur-20260630.xsd#bur_DerivativeAssetsCoreLegalFinanceEPFundsOtherAdditionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_DerivativeAssetsCoreLegalFinanceEPFundsOtherAdditionsMember" xlink:to="lab_bur_DerivativeAssetsCoreLegalFinanceEPFundsOtherAdditionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_019e415a-4dba-7805-8eb5-0ba9e8fe2eef_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross deferred tax assets</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsGross" xlink:to="lab_us-gaap_DeferredTaxAssetsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_AccruedContingentFeesReversal_019e415a-4dba-74ab-b7ff-365ad5adec64_terseLabel_en-US" xlink:label="lab_bur_AccruedContingentFeesReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent fee reversal</link:label>
    <link:label id="lab_bur_AccruedContingentFeesReversal_label_en-US" xlink:label="lab_bur_AccruedContingentFeesReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Contingent Fees Reversal</link:label>
    <link:label id="lab_bur_AccruedContingentFeesReversal_documentation_en-US" xlink:label="lab_bur_AccruedContingentFeesReversal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Contingent Fees Reversal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_AccruedContingentFeesReversal" xlink:href="bur-20260630.xsd#bur_AccruedContingentFeesReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_AccruedContingentFeesReversal" xlink:to="lab_bur_AccruedContingentFeesReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_019e415a-4e63-765c-9a9b-2737dee71f8a_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">VIE primary beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_InterestRateChangeOf50BpsMember_019e415a-4dba-70e0-af8f-85c59bb58c4e_terseLabel_en-US" xlink:label="lab_bur_InterestRateChangeOf50BpsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate 50bps</link:label>
    <link:label id="lab_bur_InterestRateChangeOf50BpsMember_label_en-US" xlink:label="lab_bur_InterestRateChangeOf50BpsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Change Of 50 bps [Member]</link:label>
    <link:label id="lab_bur_InterestRateChangeOf50BpsMember_documentation_en-US" xlink:label="lab_bur_InterestRateChangeOf50BpsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the information pertaining to change in interest rate of 50bps.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_InterestRateChangeOf50BpsMember" xlink:href="bur-20260630.xsd#bur_InterestRateChangeOf50BpsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_InterestRateChangeOf50BpsMember" xlink:to="lab_bur_InterestRateChangeOf50BpsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019e415a-4dba-7d18-bfd8-bae87526bbc0_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to Burford Capital Limited shareholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019e415a-4dba-7dfa-8707-dcd599104253_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to Burford Capital Limited shareholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019e415a-4e63-7d18-b349-9e92397bf507_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_019e415a-4e63-7b8b-ac19-677bbe5387a9_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted cash flow</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Discounted Cash Flow [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:to="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019e415a-4e63-7d55-9008-b8acd3a437c1_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInNextRolling12Months_019e415a-4dba-71b9-8bcc-536313d11526_terseLabel_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInNextRolling12Months" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInNextRolling12Months_label_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInNextRolling12Months" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Next Rolling 12 Months</link:label>
    <link:label id="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInNextRolling12Months_documentation_en-US" xlink:label="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInNextRolling12Months" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturities, Repayments Of Interest In Next Rolling 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInNextRolling12Months" xlink:href="bur-20260630.xsd#bur_LongTermDebtMaturitiesRepaymentsOfInterestInNextRolling12Months"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_LongTermDebtMaturitiesRepaymentsOfInterestInNextRolling12Months" xlink:to="lab_bur_LongTermDebtMaturitiesRepaymentsOfInterestInNextRolling12Months" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MaterialReconcilingItemsMember_019e415a-4dba-7207-84e3-9545a37eb626_terseLabel_en-US" xlink:label="lab_us-gaap_MaterialReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciling items</link:label>
    <link:label id="lab_us-gaap_MaterialReconcilingItemsMember_label_en-US" xlink:label="lab_us-gaap_MaterialReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Excluding Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MaterialReconcilingItemsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MaterialReconcilingItemsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MaterialReconcilingItemsMember" xlink:to="lab_us-gaap_MaterialReconcilingItemsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationEvents_019e415a-4dba-7c36-b220-61a119dd60be_terseLabel_en-US" xlink:label="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationEvents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of litigation events</link:label>
    <link:label id="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationEvents_label_en-US" xlink:label="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationEvents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs And Valuation Techniques, Number Of Litigation Events</link:label>
    <link:label id="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationEvents_documentation_en-US" xlink:label="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationEvents" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The number of litigation event inputs considered for measuring fair value of assets and liabilities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationEvents" xlink:href="bur-20260630.xsd#bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationEvents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationEvents" xlink:to="lab_bur_FairValueMeasurementInputsAndValuationTechniquesNumberOfLitigationEvents" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USGovernmentAgenciesShorttermDebtSecuritiesMember_019e415a-4e63-7470-b1d8-024a3d6ffdb3_terseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesShorttermDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Government securities</link:label>
    <link:label id="lab_us-gaap_USGovernmentAgenciesShorttermDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesShorttermDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government Agencies Short-Term Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USGovernmentAgenciesShorttermDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_USGovernmentAgenciesShorttermDebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USGovernmentAgenciesShorttermDebtSecuritiesMember" xlink:to="lab_us-gaap_USGovernmentAgenciesShorttermDebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CertificatesOfDepositMember_019e415a-4e63-752a-8515-15f5a2601167_terseLabel_en-US" xlink:label="lab_us-gaap_CertificatesOfDepositMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Certificates of deposit</link:label>
    <link:label id="lab_us-gaap_CertificatesOfDepositMember_label_en-US" xlink:label="lab_us-gaap_CertificatesOfDepositMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Certificates of Deposit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CertificatesOfDepositMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CertificatesOfDepositMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CertificatesOfDepositMember" xlink:to="lab_us-gaap_CertificatesOfDepositMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_019e415a-4e63-7f2a-8b53-2055c6b8856a_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of new ordinary shares to satisfy vested share-based awards</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Restricted Stock Award, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross"/>
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