I remember reading about someone telling Clapton (I think) that he would find it very hard recording with The Beatles, because they had a very different technique than to the one he was used to. Whereas his bands would go into the studio and play a song over and over until they got it right (sometimes for days), the Beatles didn't.
In their defence isn't jamming a particularly bluesy thing, and doesn't really lend itself to pop or rock (unless you play endless 12 bars, which will kill the best of men.)

Clapton was also asked to be the replacement in the Stones after Brian Jones died, but he wasn't interested in all the hoopla/weirdness that the Stones attracted. When George walked our initially, John said immediately to call Clapton.