Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in this Registration Statement on Form S-8 of Unum Therapeutics Inc. of our report dated March 2, 2018, except for the effects of the reverse stock split discussed in Note 15 to the consolidated financial statements, as to which the date is March 19, 2018, relating to the financial statements, which appears in Unum Therapeutics Inc.’s Amendment No. 1 to the Registration Statement on Form S-1 (No. 333-223414).

/s/ PricewaterhouseCoopers LLP

Boston, Massachusetts

April 3, 2018