Exhibit 10.1

BIODEXA PHARMACEUTICALS PLC

1 Caspian Point,

Caspian Way,

Cardiff, CF10 4DQ, United Kingdom

September 14, 2026

To the Holder of Series M Warrants, Series N Warrants and Series O Warrants of Biodexa Pharmaceuticals PLC, each to Purchase Ordinary Shares Represented by American Depositary Shares

Dear Holder:

BIODEXA PHARMACEUTICALS PLC (the “Company”) is pleased to offer to you (the “Holder,” “you” or similar terminology) the opportunity to receive new warrants to purchase ordinary shares, nominal value £0.000001 per share, of the Company (the “Ordinary Shares”) represented by American Depositary Shares of the Company (the “ADSs”) in consideration for you exercising for cash all of the Series M Warrants, Series N Warrants, and Series O Warrants to purchase Ordinary Shares represented by ADSs held by you (“Existing Warrants”) as set forth on your signature page hereto. The issuance and/or the resale of the Ordinary Shares represented by ADSs underlying the Existing Warrants (the “Warrant ADSs”) have been registered pursuant to the Company’s registration statement on Form F-1 (File No. 333-297473) (the “Registration Statement”). The Registration Statement is currently effective and, upon exercise of the Existing Warrants pursuant to this letter agreement, will be effective for the resale or issuance, as the case may be, of the Warrant ADSs if sold pursuant thereto. Capitalized terms not otherwise defined herein shall have the meanings set forth in the New Warrants (as defined hereinafter).

In consideration for exercising the Existing Warrants held by you and set forth on the Holder’s signature page hereto (the “Warrant Exercise”) at the reduced exercise price per Warrant ADS of $1.05 for the Existing Warrants, the Company hereby offers to issue to you or your designee a new unregistered Series P purchase warrant to purchase Ordinary Shares represented by ADSs (“New Warrants”) pursuant to Section 4(a)(2) of the Securities Act of 1933, as amended (“Securities Act”), to purchase up to a number of Ordinary Shares represented by ADSs (the “New Warrant ADSs”) equal to 200% of the number of Warrant ADSs issued pursuant to each Warrant Exercise hereunder, which New Warrants shall be substantially in the form as set forth in Exhibit A hereto, for $1.05 per ADS, subject to adjustment as provided in the New Warrants. Such New Warrants will be immediately exercisable and have a term of exercise of five (5) years from the date of issuance.

The New Warrant certificates will be delivered within one (1) Trading Day following the date hereof, and such New Warrants underlying Ordinary Shares represented by ADSs issued upon exercise of the New Warrants, will, unless and until registered, contain customary restrictive legends and other language typical for an unregistered warrant and unregistered Ordinary Shares represented by ADSs. Notwithstanding anything herein to the contrary, in the event that any Warrant Exercise would otherwise cause the Holder to exceed the beneficial ownership limitations (“Beneficial Ownership Limitation”) set forth in Section 2(e) of the Existing Warrants (or, if applicable and at the Holder’s election, 9.99%), the Company shall only issue such number of Warrant ADSs to the Holder that would not cause the Holder to exceed the maximum number of Ordinary Shares and/or ADSs permitted thereunder, as directed by the Holder, with the balance to be held in abeyance until notice from the Holder that the balance (or portion thereof) may be issued in compliance with such limitations, which abeyance shall be evidenced through the Existing Warrants which shall be deemed prepaid thereafter (including the payment in full of the exercise price), and exercised pursuant to a Notice of Exercise in the Existing Warrants (provided that no additional exercise price shall be due and payable). The parties hereby agree that the Beneficial Ownership Limitation for purposes of the Existing Warrants is as set forth on the Holder’s signature page hereto.

Expressly subject to the paragraph immediately following this paragraph below, the Holder may accept this offer by signing this letter below, with such acceptance constituting the Holder’s exercise in full of the Existing Warrants for an aggregate exercise price set forth on the Holder’s signature page hereto (the “Warrants Exercise Price”) on or before 7:30 a.m., Eastern Time, on September 15, 2026 (the “Execution Time”).

The Company agrees to the representations, warranties and covenants set forth on Annex A attached hereto.

Holder represents and warrants that, as of the date hereof it is, and on each date on which it exercises any New Warrants it will be, an “accredited investor” as defined in Rule 501 of Regulation D promulgated under the Securities Act, and agrees that, when issued, the New Warrants will contain customary restrictive legends, and neither the New Warrants nor the Ordinary Shares represented by ADSs issuable upon exercise of the New Warrants will be registered under the Securities Act, except as provided in Annex A attached hereto. Also, Holder represents and warrants that it is acquiring the New Warrants as principal for its own account and has no direct or indirect arrangement or understandings with any other persons to distribute or regarding the distribution of the New Warrants or the New Warrant ADSs (this representation is not limiting Holder’s right to sell the New Warrant ADSs pursuant to an effective registration statement under the Securities Act or otherwise in compliance with applicable federal and state securities laws).

The Holder understands that the New Warrants and the New Warrant ADSs are not, and may never be, registered under the Securities Act, or the securities laws of any state and, accordingly, each certificate, if any, representing such securities shall bear a legend substantially similar to the following:

THIS SECURITY HAS NOT BEEN REGISTERED WITH THE SECURITIES AND EXCHANGE COMMISSION OR THE SECURITIES COMMISSION OF ANY STATE IN RELIANCE UPON AN EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR PURSUANT TO AN AVAILABLE EXEMPTION FROM, OR IN A TRANSACTION NOT SUBJECT TO, THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND IN ACCORDANCE WITH APPLICABLE STATE SECURITIES LAWS.

Upon the Holder’s exercise of the New Warrants, certificates evidencing the New Warrant ADSs shall not contain any legend (including the legend set forth above), (i) while a registration statement covering the resale of such New Warrant ADSs is effective under the Securities Act, (ii) following any sale of such New Warrant ADSs pursuant to Rule 144 under the Securities Act, (iii) if such New Warrant ADSs are eligible for sale under Rule 144 (assuming cashless exercise of the New Warrants), without the requirement for the Company to be in compliance with the current public information requirement under Rule 144 as to such New Warrant ADSs and without volume or manner-of-sale restrictions, (iv) if such New Warrant ADSs may be sold under Rule 144 (assuming cashless exercise of the New Warrants) and the Company is then in compliance with the current public information requirement under Rule 144 as to such New Warrant ADSs, or (v) if such legend is not required under applicable requirements of the Securities Act (including judicial interpretations and pronouncements issued by the staff of the Securities and Exchange Commission (the “Commission”) and the earliest of clauses (i) through (v), the “Delegend Date”)). The Company shall cause its counsel to issue a legal opinion to the Transfer Agent promptly after the Delegend Date if required by the Company and/or the Transfer Agent to effect the removal of the legend hereunder, or at the request of the Holder, which opinion shall be in form and substance reasonably acceptable to the Holder. From and after the Delegend Date, such New Warrant ADSs shall be issued free of all legends, provided, that, upon request of the Company (which request shall include a form of customary representation letter), the Holder has delivered in advance to the Company a customary representation letter that is reasonably satisfactory to the Company and its counsel and the Transfer Agent. The Company agrees that following the Delegend Date or at such time as such legend is no longer required under this Section, it will, no later than one (1) Trading Day following the delivery by the Holder to the Company or the Transfer Agent of a certificate representing the New Warrant ADSs issued with a restrictive legend (such first (1^st) Trading Day, the “Legend Removal Date”), deliver or cause to be delivered to the Holder a certificate representing such shares that is free from all restrictive and other legends or, at the request of the Holder, shall credit the account of the Holder’s prime broker with the Depository Trust Company System as directed by the Holder.

In addition to the Holder’s other available remedies, the Company shall pay to a Holder, in cash, (i) as partial liquidated damages and not as a penalty, for each $1,000 of New Warrant ADSs (based on the VWAP of the ADSs on the date such New Warrant ADSs are submitted to the Transfer Agent) delivered for removal of the restrictive legend, $10 per Trading Day (increasing to $20 per Trading Day five (5) Trading Days after such damages have begun to accrue) for each Trading Day after the Legend Removal Date until such certificate is delivered without a legend and (ii) if the Company fails to (a) issue and deliver (or cause to be delivered) to the Holder by the Legend Removal Date a certificate representing the New Warrant ADSs free from all restrictive and other legends and (b) if after the Legend Removal Date the Holder purchases (in an open market transaction or otherwise) ADSs to deliver in satisfaction of a sale by the Holder of all or any portion of the number of ADSs, or a sale of a number of ADSs equal to all or any portion of the number of ADSs that the Holder anticipated receiving from the Company without any restrictive legend, then, an amount equal to the excess of the Holder’s total purchase price (including brokerage commissions and other out-of-pocket expenses, if any) for the ADSs so purchased (including brokerage commissions and other out-of-pocket expenses, if any) (the “Buy-In Price”) over the product of (A) such number of New Warrant ADSs that the Company was required to deliver to the Holder by the Legend Removal Date and for which the Holder was required to purchase shares to timely satisfy delivery requirements, multiplied by (B) the weighted average price at which the Holder sold that number of ADSs. For purposes herein, “Transfer Agent” means the Depositary (as such term is defined in the New Warrants).

If this offer is accepted and this letter agreement is executed by the Execution Time, then on or before 8:30 a.m., Eastern Time, on the Trading Day following the date hereof, the Company shall issue a press release and/or file a Report on Form 6-K with the Commission disclosing all material terms of the transactions contemplated hereunder, including this letter agreement as an exhibit thereto with the Commission within the time required by the Exchange Act. From and after the issuance of such press release or filing of such of such Report on Form 6-K, as applicable, the Company represents to you that it shall have publicly disclosed all material, non-public information delivered to you by the Company, or any of its respective officers, directors, employees or agents in connection with the transactions contemplated hereunder. In addition, effective upon the issuance of such press release and/or filing of such Report on Form 6-K, the Company acknowledges and agrees that any and all confidentiality or similar obligations under any agreement, whether written or oral, between the Company, any of its Subsidiaries or any of their respective officers, directors, agents, employees or Affiliates on the one hand, and you and your Affiliates on the other hand, shall terminate. The Company represents, warrants and covenants that, upon acceptance of this offer, the Warrant ADSs issuable upon your exercise of the Existing Warrants shall be issued free of any legends or restrictions on resale by Holder.

No later than the first (1^st) Trading Day following the date hereof, the closing (“Closing”) shall occur at such location as the parties shall mutually agree. Unless otherwise directed by Maxim Group LLC (the “Placement Agent”), settlement of the Warrant ADSs shall occur via “Delivery Versus Payment” (“DVP”) (i.e., on the Closing Date, the Company shall issue the Warrant ADSs registered in the Holder’s name and address provided to the Company in writing and released by the Depositary directly to the account(s) at the Placement Agent identified by the Holder; upon receipt of such Warrant ADSs, the Placement Agent shall promptly electronically deliver such Warrant ADSs to the Holder, and payment therefor shall concurrently be made to the Company by the Placement Agent (or its clearing firm) by wire transfer to the Company). The date of the Closing of the exercise of the Existing Warrants shall be referred to as the “Closing Date.”

[Holder Signature Page Follows]

[Signature Page to BDRX Inducement Letter]

Accepted and Agreed to:

Aggregate Warrant Exercise Price at the Reduced Exercise Price being exercised contemporaneously with signing this letter agreement: _________________________________________________

Existing Warrants Beneficial Ownership Blocker: 4.99% or 9.99%

New Warrants Beneficial Ownership Blocker: 4.99% or 9.99%

[Signature Page to BDRX Inducement Letter]

Annex A

Representations, Warranties and Covenants of the Company. The Company hereby makes the following representations and warranties to the Holder:

a)        SEC Reports. The Company has filed all reports, schedules, forms, statements and other documents required to be filed by the Company under the Exchange Act, including pursuant to Section 13(a) or 15(d) thereof, for the two years preceding the date hereof (or such shorter period as the Company was required by law or regulation to file such material) (the foregoing materials, including the exhibits thereto and documents incorporated by reference therein “SEC Reports”). As of their respective dates, the SEC Reports complied in all material respects with the requirements of the Exchange Act and none of the SEC Reports, when filed, contained any untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading except as otherwise noted in a subsequent SEC Report. The Company has never been an issuer subject to Rule 144(i) under the Securities Act.

b)        Authorization; Enforcement. The Company has the requisite corporate power and authority to enter into and to consummate the transactions contemplated by this letter agreement and otherwise to carry out its obligations hereunder. The execution and delivery of this letter agreement by the Company and the consummation by the Company of the transactions contemplated hereby have been duly authorized by all necessary action on the part of the Company, and no further action is required by the Company, its board of directors or its stockholders in connection herewith. This letter agreement has been duly executed by the Company and, when delivered in accordance with the terms hereof, will constitute the valid and binding obligation of the Company enforceable against the Company in accordance with its terms, except (i) as limited by general equitable principles and applicable bankruptcy, insolvency, reorganization, moratorium and other laws of general application affecting enforcement of creditors’ rights generally, (ii) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies and (iii) insofar as indemnification and contribution provisions may be limited by applicable law. The New Warrants have been duly authorized and, when issued and delivered in accordance with this letter agreement, will be validly issued, and the Ordinary Shares underlying the New Warrant ADSs have been duly authorized.

c)        No Conflicts. The execution, delivery and performance of this letter agreement by the Company and the consummation by the Company of the transactions contemplated hereby do not and will not: (i) conflict with or violate any provision of the Company’s certificate or articles of incorporation, bylaws or other organizational or charter documents; or (ii) conflict with, or constitute a default (or an event that with notice or lapse of time or both would become a default) under, result in the creation of any liens, claims, security interests, other encumbrances or defects upon any of the properties or assets of the Company in connection with, or give to others any rights of termination, amendment, acceleration or cancellation (with or without notice, lapse of time or both) of, any material agreement, credit facility, debt or other material instrument (evidencing Company debt or otherwise) or other material understanding to which such Company is a party or by which any property or asset of the Company is bound or affected; or (iii) conflict with or result in a violation of any law, rule, regulation, order, judgment, injunction, decree or other restriction of any court or governmental authority to which the Company is subject (including federal and state securities laws and regulations), or by which any property or asset of the Company is bound or affected, except, in the case of each of clauses (ii) and (iii), such as could not have or reasonably be expected to result in a material adverse effect upon the business, prospects, properties, operations, condition (financial or otherwise) or results of operations of the Company, taken as a whole, or in its ability to perform its obligations under this letter agreement.

d)        Registration Obligations. As soon as practicable (and in any event within 15 calendar days of the date hereof), the Company shall file a registration statement on Form F-1 or Form F-3 providing for the resale by the Holder of the Ordinary Shares represented by the New Warrant ADSs issued and issuable upon exercise of the New Warrants. The Company shall use commercially reasonable efforts to cause such registration to become effective within 45 days of the Closing Date (75 days from the Closing Date in the event the Commission elects to review such registration statement) and to keep such registration statement effective at all times until the Holder does not own any New Warrants or New Warrant ADSs issuable upon exercise thereof. The Holder agrees to properly notify the Company if it no longer owns any New Warrants or New Warrant ADSs issuable upon exercise thereof.

e)        Trading Market. The transactions contemplated under this letter agreement comply with all the rules and regulations of the Nasdaq Capital Market.

f)        Filings, Consents and Approvals. The Company is not required to obtain any consent, waiver, authorization or order of, give any notice to, or make any filing or registration with, any court or other federal, state, local or other governmental authority or other Person in connection with the execution, delivery and performance by the Company of this letter agreement, other than: (i) the filings required pursuant to this letter agreement; (ii) application(s) or notice to each applicable Trading Market for the listing of the New Warrants and New Warrant ADSs for trading thereon in the time and manner required thereby, and (iii) the filing of Form D with the Commission and such filings as are required to be made under applicable state securities laws.

g)        Listing of ADSs. The Company hereby agrees to use best efforts to maintain the listing or quotation of the ADSs on the Trading Market on which it is currently listed, and concurrently with the Closing, the Company shall apply to list or quote all of the New Warrant ADSs on such Trading Market and promptly secure the listing of all of the New Warrant ADSs on such Trading Market. The Company further agrees, if the Company applies to have the ADSs listed on any other Trading Market, it will then include in such application all of the New Warrant ADSs, and will take such other action as is necessary to cause all of the New Warrant ADSs to be listed or quoted on such other Trading Market as promptly as possible. The Company will then take all action reasonably necessary to continue the listing and trading of its ADSs on a Trading Market and will comply in all respects with the Company’s reporting, filing and other obligations under the bylaws or rules of the Trading Market. The Company agrees to maintain the eligibility of the ADSs for electronic transfer through the Depository Trust Company or another established clearing corporation, including, without limitation, by timely payment of fees to the Depository Trust Company or such other established clearing corporation in connection with such electronic transfer.

h)        Form D; Blue Sky Filings. If required, the Company agrees to timely file a Form D with respect to the New Warrants and New Warrant ADSs as required under Regulation D and to provide a copy thereof, promptly upon request of the Holder. The Company shall take such action as the Company shall reasonably determine is necessary in order to obtain an exemption for, or to qualify the New Warrants and New Warrant ADSs for, sale to the Holder at Closing under applicable securities or “Blue Sky” laws of the states of the United States, and shall provide evidence of such actions promptly upon request of any Holder.

Exhibit A

Form of new warrant

(See attached)