So I've been thinkign that this is clearly the Kinks, who should by rights be considered up there there with the Stones in terms of influence. Sure they were quite successful and most people know them because of Lola, but there's so much more to them than a song about a dude in a dress.
For example:
Those are from 1964 and 1965!!!! They were rocking out like that while the Beatles still sounded like the f**king Monkeys.
A little less rocky, but note the slide guitar long before Duane Allman carved a guitar out of an old tree stump:
Also probably the coolest song to feature a girls name in the title.
Basically the Kinks > who you were thinking.