Exhibit 13.1

CERTIFICATION OF PRINCIPAL EXECUTIVE 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 Achilles Therapeutics plc (the “Company”) for the year ended December 31, 2023 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned officer hereby certifies pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to the best of his knowledge:

(1) the 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 Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: April 4, 2024

By:	/s/ Iraj Ali
	Name: Iraj Ali
	Title: Chief Executive Officer (Principal Executive Officer)