http://www.bromptondock.co.uk/
Register at the URL above. Pack light. Catch your plane to Heathrow. When you clear customs, send a text to reserve your bike. Take the Heathrow Connect or Piccadilly/District underground to Ealing Broadway (get a pay-as-you-go oyster card at the same time). Go collect your bike.
£10 for a week's "trial" hire. Enjoy!
(caveats: I haven't done this, so don't know the problems; Does it work with overseas credit cards? - probably, as it accepts overseas mobiles; Will there be a bike available when you arrive? Do you really want to learn about London traffic, brompton handling, riding on the left etc etc with jet lag?)