I don't often see too many passengers on this route, but I do see plenty of air crew use it, so I would like to suggest another option to get into London which is just as cheap as the tube.
There's a train service that runs from Waterloo via Clapham Junction to Feltham. From Feltham there's a 20 minute bus ride - 285- into LHR (although it can sometimes take 40 minutes if there's a lot of congestion at the airport, but you're going to be in the same traffic jam as everybody in the courtesy buses that serve the airport hotels).
It means that you should be able to get from LHR to the city in less than an hour (Waterloo is just a short ride away from Bank Station)
It starts running earlier than the tubes and will allow you to get to Heathrow for 06:30.
The train service can be erratic, and it's best to check how many stops the train will make - the Feltham-Waterloo train journey takes between 25 and 50 mins + depending on the train.
So, yes, it is a wee bit complicated and all this probably explains why air crew use this service rather than pax, but it is a good option to have under your belt when there's a tube strike, need to get to the city in a hurry, or if you're a budget traveller trying to get from LHR to Stansted (via Liverpool Street) quickly and cheaply.
Definitely one to consider as an alternative to a coach trip into the capital.
It is pretty difficult to get info on the service - but I did find this (as well as a document by the LHR Passengers's committee expressing concern at the lack of publicity for the service by South West Rail and Anglia Railways)
"Also available is the Heathrow-Feltham Rail Air express bus link, which connects Feltham rail station to Heathrow Airport and providesa valuable link to and from rail services on the local and national rail network from Feltham, Reading, Woking and Watford Junction. For further information about this service call London Transport information on +44 (0)20 7222 1234."
One last tip: a really user friendly rail timetable services can be found at
www.bahn.de There's a small ENGLISH icon on the left. I find it easier to use and more accurate than the British National Rail timetable web page.