IMO The Spinners were not (by and large) great musicians or singers, but as others have said, they conveyed their enthusiasm for the songs they sang, and encouraged audience participation, which had become a bit of a rarity back then, except in folk clubs, so they caught on with the mainstream public.

They had a knack of finding good songs too (although I didn't like all their output, by any means) - maybe if they 'pinched' other peoples' songs, it could explain some of the animosity towards them from certain quarters of the folk world. This is just speculation on my part, I hasten to add, and I don't know of any examples where this happened.