If your going to london anytime soon and you are not carrying a lot of things then I extremely recommend getting the Virgin Limobikes. Im going to try this as soon as I go to London, they do airport transport or in London transport. I was surprised about how reasonably priced they are compared to taxis.
They can get you anywhere in 20 mins in town since they get around traffic very easily and get to the front. They also have enough area to carry some small bags nothing too big. I recommend one friend to do this already and he had a blast, he told me that was the most exciting thing he has done in London in a long time. He managed to get to a meeting in under 10mins and they got him home in under 15 mins which usually takes 25 mins if he is lucky. And these guys are experts in city traffic riding. They also take Richard Bronson from point to point sometimes. The cost is reasonable ranging from £25 to £40 when your in and around London, and transport to Heathrow from London is £60 which is extremely reasonable for getting you there in amazing time. Try it people you wont regret it.
Link: VirgiLimoBikes