Even though David Beckham and his wife Posh Spice are moving to sunny LA - it's still a great time to buy for an expat to buy a flat in London.
First figure out where you want to live in London. Chelsea is the capital of the expats - anywhere along the Fulham Road and you can't go wrong.
Make an offer on the flat. Be aware that unlike other markets (United States, for example) your bid can get trumped at any time prior to exchanging contracts. Also, be aware that you need to pay Stamp Tax, which in the UK is 4% of the purchase price. God save the Queeen. Most lenders will roll this into the loan. When you sell, the sellers commission is only about 2%, so net net the transaction expense equal 6%, which is roughly the equivalent of what you'd pay in the US.
Avoid leaseholds if you can. Expats have a hard time understanding that you don't really own the flat, you have a 999 year lease (yes, nine hundred ninety-nine years- only in the UK!)
Figure out how much you want to borrow and start talking to places like Woolich - online sites abound with great information.
Borrow as much as you can with an interest-only mortgage. You are unlikely to ever pay off the mortgage - go ahead, live a little.
Have a 'solicitor' due his evaluation on the property and contracts. Solicitor is a fancy word for lawyer.
Exchange contracts, order the champagne, and celebrate!