Sloops, OPVs, and global presence missions

Would a continuing British Empire have retained or built more OPV-type ships?

Yes. A global empire would retain sloop-like presence ships, even if later terminology called them patrol vessels or OPVs.

A sloop is built around presence, shallow-water access, and long-distance imperial policing rather than high-end escort warfare. The postwar Type 81 illustrates how calling a presence ship a frigate can invite expectations it was not designed to meet. In an empire-retaining alternate history, the sloop mission would persist even if later terminology called the ships patrol vessels or OPVs. Their combination of ocean endurance and access to shallow coastal or river waters made them especially useful instruments of naval diplomacy.