London Walks are *the* walking tour company. Accept no substitutes!
I know, these guys get splashed all over the guide books, but they really are excellent - and not just for tourists. Some of the west-end ones are weighted that way more than the rest, but I've been on a good number of London Walks walks, always learned something, and never been the only Londoner in the party.
(I wanted to link you to the upcoming Story of London Walking Weekend on the 6th/7th, but as there's exactly no information about the specifics on the site, there's not much point. I'll report back when that changes!)