Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the registration statements (Nos. 333-203929 and 333-233558) on Form S-8 and (No. 333-264208) on Form S-3 of Adaptimmune Therapeutics plc of our report dated March 23, 2023, with respect to the consolidated financial statements of TCR² Therapeutics Inc. which report is incorporated by reference in the Form 8-K of Adaptimmune Therapeutics plc dated August 10, 2023.

/s/ KPMG LLP

Boston, Massachusetts

August 10, 2023