Exhibit 5.1 May 13, 2024 Summit Therapeutics Inc. 601 Brickell Key Drive, Suite 1000 Miami, FL 33131 Ladies and Gentlemen: We have acted as counsel to Summit Therapeutics Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-3 (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission (the “Commission”) on February 20, 2024 and declared effective on February 27, 2024 and the Prospectus Supplement, dated May 13, 2024 (the “Prospectus Supplement”). The Prospectus Supplement relates to the offer and sale from time to time of shares of the Company’s common stock, par value $0.01 per share (the “Common Stock”), up to a maximum aggregate amount of $90.0 million (the “Shares”), pursuant to a Distribution Agreement, dated May 13, 2024, between the Company and J.P. Morgan Securities LLC. We have examined such documents and such matters of fact and law as we deem necessary to render the opinions contained herein. In our examination, we have assumed, but have not independently verified, the genuineness of all signatures, the conformity to original documents of all documents submitted to us as certified, facsimile or other copies, and the authenticity of all such documents. As to questions of fact material to this opinion, we have relied on certificates or comparable documents of public officials and of officers and representatives of the Company. For purposes of this opinion, we have assumed that: (a) the Registration Statement will remain effective at the time of issuance and sale of the Shares; (b) the Shares will be sold at prices and other terms authorized by the Company’s Board of Directors or another duly authorized committee thereof; and (c) at the time of the issuance and sale of the Shares, a sufficient number of shares of Common Stock will remain authorized and available for issuance pursuant to the Company’s Amended and Restated Certificate of Incorporation, as it then may be amended.

4857-6129-0429.2 Based on the foregoing, and subject to the qualifications stated herein, we are of the opinion that the Shares offered pursuant to the Prospectus Supplement will be validly issued, fully paid and non-assessable. The opinions expressed herein are limited to the General Corporation Law of the State of Delaware and we express no opinion as to the effect on the matters covered by this letter of the laws of any other jurisdiction. We hereby consent to the filing of this letter as Exhibit 5.1 to a Current Report on Form 8- K that will be filed by the Company and incorporated by reference into the Registration Statement and to the reference to our firm in the Prospectus Supplement under the heading “Legal Matters.” In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the Commission. Very truly yours, /s/ Baker & Hostetler LLP BAKER & HOSTETLER LLP