and yeah, it's killer expensive.
Unfortunately, I can only echo what others have already said. Pub food is cheaper. If you can, find a hotel with a continental breakfast...then you've got one meal already taken care of.
We stayed at the St. Giles Hotel near the Tottenham Court Road station and it was relatively cheap, without being skanky. It's also centrally located, just get a pass for the Underground and your transportation is taken care of.
If you're at all interested in musical theater, hit up Leicester Square for discounted tickets. I *HIGHLY* recommend Wicked. It's fabulous, and the person who plays Elphaba (the Wicked Witch) in the London cast is phenomenal.
The museums are free...and world-class, obviously.
If you're totally new to the city and don't know where things are located, I recommend popping for a sightseeing trip on the original London bus tour (or similar). You get to ride around the city on one of those infamous double-decker buses, and you get a really good feel for the layout of the city. Also, you can hop on/hop off as many times as you want for free...and the ticket is valid for 24-hours. Also, the vendors that sell the bus tickets sometimes have deals for tickets to other tourist traps...err...sights. ;) We started our tour at Trafalgar Square, the far corner, by the statue of the lady with no arms. It costs about 17 pounds.
http://www.theoriginaltour.com/Have fun! :D