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. 333-275813, 333-233558 and 333-203929 on Form S-8, of our report dated March 6, 2024, with respect to the consolidated financial statements of Adaptimmune Therapeutics plc.

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/s/ KPMG LLP

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Reading, United Kingdom

March 6, 2024