It's interesting that a couple of people mentioned The Animals above, in the context of R&R. I wouldn't have categorised them that way, as they came later (first 'proper' record not issued until 1964). They were one of the leading bands in the UK 'R&B' boom of the early/mid 1960s. (R&B = Rhythm & Blues, not to be confused with the very different stuff today that uses that same label).

I was a great fan of the Animals, Yardbirds, Georgie Fame & The Blue Flames, Downliners Sect and other bands around that time (1964-5). Indeed, the Rolling Stones were in that category in their early days.

But I wouldn't have said these were (at least, primarily) R&R bands (although admittedly, the Animals, Yardbirds, Stones and others did record some R&R songs by Chuck Berry, etc.).