Tube (journey time to central London is about 60 minutes) : The airport is served by the Piccadilly Line Underground. Trains leave from Heathrow Central (from Terminals 1-3). Terminals 4 and 5 each have their own station.
Some metro carriages serve Terminals 1-3 and 5. Others just terminal 4. At the Boston Manner metro station just before Heathrow, you should change carriage if you metro train isn't going to the terminal you want to go to.