Exhibit 23.1

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Consent of Independent Registered Public Accounting Firm

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We consent to the incorporation by reference in the registration statements No.333-264208 on Form S-3 and Nos. 333-233558 and 333-203929 on Form S-8 of Adaptimmune Therapeutics plc of our reports dated March 6, 2023, with respect to the consolidated financial statements of Adaptimmune Therapeutics plc and the effectiveness of internal control over financial reporting which reports appear in the Form 10-K of Adaptimmune Therapeutics plc dated March 6, 2023.

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/s/ KPMG LLP

Reading, United Kingdom

November 14, 2023