London is one of my favorite cities. Where do I start? By seconding everyting that has already been said.
There was a book reviewed in the paper, called
Secret London, by Andrew Duncan. That might give you some ideas off the beaten path.
Many years ago I went to the Sherlock Holmes Pub, as I am a fan. Nice display of his study.
Bath is great, or you could do Stonehenge. It isn't that much farther.
Have a good time!
Frances