I've never been into Beck and Clapton that much, and Page is my favorite musician, ever - but I wouldn't necessarily think he's the greatest guitarist of them all.
Though I'm a guitar player, I realize that I mostly don't care for "best guitar player" type of things. I have a bunch of favorite players, and they may happen to be technically great, but that's not a criteria.
Attitude and taking chances are two qualities I associate Page with, and I think I remember reading an interview with Van Halen in which he mentioned that even though he'd studied Clapton note for note, Page's attitude and sense of fun had tremendously influenced him.
My list of classic English guitar players would probably start w/ Page and Gilmour. Mick Ronson would also be there. Adrian Smith. Soulful players.