QuickLinks -- Click here to rapidly navigate through this document

Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

        We consent to the reference to our firm under the caption "Experts" in Amendment No. 1 to the Registration Statement (Form S-11 No. 333-231224) and related Prospectus of Tremont Mortgage Trust for the registration of its common shares of beneficial interest and to the incorporation by reference therein of our report dated February 7, 2019, with respect to the consolidated financial statements of Tremont Mortgage Trust included in its Annual Report (Form 10-K) for the year ended December 31, 2018, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Boston, Massachusetts
May 14, 2019

QuickLinks

Exhibit 23.1