London is great, been there twice now and still barely scratched the surface. Though I was barely in London last year (spent most of my time at the races outside London). But most of the places I went in '09 were name checked already - The Eye, Tower of London, Victoria & Albert Museum, Hyde/Regent Park, and Greenwich. It's a great city to walk around and all the public transportation is a major plus. Not a foodie, so I don't have any recs on that.
Next time I want to do as a side trip is Windsor Castle and/or Hampton Court as I am fascinated by all the historical places.
As for the fuel charges - no free lunch - you're gonna have to pay something, but flying BA is the most expensive. Basically, you want AA (or some other partner airline like Iberia or Air Berlin) flights and take a train out of the UK to fly home from another EU country will knock it even lower.
See this:
http://www.flyertalk.com/forum/ameri...er-thread.html