I never heard Tubby play better than on his New York Sessions with Clark Terry. IMHO, American rhythm sections gave him what he needed.
There is one wonderful exception to what you say. In May '62, Hayes fronted a British quintet including Jimmy Deuchar on trumpet, for a live date at Ronnie Scott's in London. The material recorded is spread over two CDs, "Late Spot at Scott's" and "Down in the Village" on the ReDial label. Truly fabulous music with great arrangements - the version of "Johnny One Note" is truly hair raising (what I have left of it) - the best Hayes ever recorded IMO, and the rhythm section totally cooks. I've played this music for very knowledgeable friends and no one picks up on the fact that it's a non-American rhythm section.
Agreed. I have both of those albums and like them very much. But Tubbs is on record - in interview with Les Tomkins, if I remember correctly - expressing his misgivings about some British drummers of those days.