Travelling to Heathrow from Central London - Use Heathrow Express from Paddington Station
Trust me - quicker than the underground and much cheaper and quicker than a taxi. £29 return from Paddington Station - stops at Terminals 1, 2, 3 and then Terminal 4. Loads of space for your luggage, WiFi available (T-mobile hotspot) on board and it takes just 15 minutes.
Well worth the £29 return. I live here and I always use this to get to and from Heathrow Airport.
There is also an express train between Victoria and Gatwick Airport - this takes 30 minutes.
This tip has the address "Paddington Station & London Heathrow Airport (LHR)"