Exhibit 13.1

Certification by the Principal Executive Officer and Principal Financial Officer pursuant to

18 U.S.C. Section 1350, as adopted pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Annual Report on Form 20-F of Immunocore Holdings plc (the “Company”)  for the fiscal year ended December 31, 2020 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Bahija Jallal, Chief Executive Officer of the Company and Brian Di Donato,  Chief Financial Officer of the Company, pursuant to 18 U.S.C. § 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, each hereby certifies that, to the best of her or his knowledge:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

Date: March 25, 2021

/s/ Bahija Jallal, Ph.D.

Chief Executive Officer

(Principal Executive Officer)

/s/ Brian Di Donato

Chief Financial Officer

(Principal Financial Officer)