Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

The Board of Directors

Adaptimmune Therapeutics plc:

We consent to the use of our reports with respect to the consolidated financial statements and the effectiveness of internal control over financial reporting incorporated by reference herein and to the reference to our firm under the heading ‘Experts’ in the prospectus. Our report dated February 27, 2020 on the 2019 consolidated financial statements refers to a change in the method of accounting for leases as of January 1, 2019 due to the adoption of Accounting Standard Codification Topic 842, Leases, and a change to the method of accounting for revenue from contracts with customers as of January 1, 2018 due to the adoption of the Accounting Standard Codification Topic 606, Revenue from Contracts with Customers).

/s/ KPMG LLP

Reading, United Kingdom

August 10, 2020