Exhibit 32.1

Section 906 Certificate

Certification Pursuant to 18 U.S.C. Section 1350, as Adopted Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code), I, Adrian Rawcliffe, Chief Executive Officer of Adaptimmune Therapeutics plc, a public limited company incorporated under English law (the “Company”), hereby certify, to my knowledge, that:

1. The Company’s annual report on Form 10-K for the year ended December 31, 2021, to which this Certification is attached as Exhibit 32.1 (the “Annual Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Annual Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: March 14, 2022

/s/ Adrian Rawcliffe

Adrian Rawcliffe

Chief Executive Officer and Director