Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statement on Form S-8 (File No. 333-225720) and the Registration Statement on Form S-3 (File No. 333-234286) of Cambridge Bancorp therein of our report dated March 29, 2019, with respect to the consolidated financial statements of Wellesley Bancorp, Inc. included in its Annual Report on Form 10-K for the year ended December 31, 2018.

/s/ Wolf & Company, P.C.

Boston, Massachusetts

December 5, 2019