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. 333-233557 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.

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/s/ KPMG LLP

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Reading, United Kingdom

March 6, 2023