Here is a link:

http://www.airwise.com/airports/euro.../LHRtran1.html

...Heathrow has two rail services to central London. In addition to the London Underground ( "the tube" ) is the Heathrow Express service to London Paddington station.....

I always use the Underground. Other FFs on the board like the Paddigton connection.
It depends a bit which terminal you arrive and where you want to go in London.
If I remember it right, the tube station is very far from LHR terminal 3.