Actually, the Fat Duck is just outside of London in Bray.
I've not been, but was invited by a group of friends a few years ago.
It was, obviously, a bit pricey, and having just moved into a flat in London, I didn't really want to spend the money.
I sorely regretted not going afterwards though, as it's definitely more of an experience than just good food. Each course is sort of a show, with great attention to detail and craftsmanship. Just watch an episode of "Heston's Feasts" and you will get an idea. In fact, one of the dishes he did on the show, Mock Turtle Soup, was a dish served to my friends.
You can also try the pub next door to The Fat Duck, The Hinds Head, also run by Heston. Apparently, it's pretty fantastic, cheaper, and easier to get a booking for.