How about the Beatles imitating Elmore James, as they imply in one their songs.
Yeah. That was George Harrison at the intro of "For You Blue," from _Let It Be_.
The Beatles were influenced by many different artists, but very few were their contemporaries. Aside from the rivalry with the Rolling Stones, which I don't think mattered much, the only important contemporary influences that I know about were Bob Dylan and Brian Wilson/the Beach Boys.
(Of course, Ravi Shankar was a significant influence on GH, but he was significantly older, too.)
Speaking of influences, are you familiar with "Belly Button Window" from Jimi Hendrix's _The Cry of Love_? He's doing his own Dylan song there.