Though I'm more a fan of their older stuff, the Stones never fully pulled me in. Same with the Beatles, but opposite (I tend to like their later works). And no, I'm not an Elvis fan, either. I had a very complicated relationship with classic rock growing up, which didn't change til my dad watched me watching Delicate Sound Of Thunder on VHS back in the day. that's when it started becoming OK.
Picking old British acts: I have to go with Traffic, Jethro Tull, Pink Floyd, Cream... True 1967-73 Psychedelia. And Psychedelic Blues.