Exhibit 32.1

Certification of Chief 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 of Rockley Photonics Holdings Limited (the “Company”) on Form 10-K for the period ended December 31, 2022, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

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 result of operations of the Company as of and for the period covered by the Report.

/s/ Dr. Andrew Rickman, OBE

Dr. Andrew Rickman, OBE

Chief Executive Officer

(Principal Executive Officer)

Date: May 15, 2023