Having started this subject, I'd like to add some more comments. In principle I agree with reducing traffic and moving people to public transport. If congestion charging is to be one of the tools, so be it.
I live no more that 20 miles from Heathrow. To get to Heathrow I can:
1) Drive
2) Take a taxi (GBP20.00?)
3) Take a public bus (not a coach) fare unknown, journey time over one hour, runs every 30 minutes but only between 0700 and 1800.
4) Take a train, change to a public bus.
For options 3 and 4 I have to make my way to the appropriate departure point (with luggage) before I start the journey proper.
Given the cost of parking at LHR I tend to take a taxi for anything more than a 3 day trip. Very convenient for me and the extra GBP10 isn't going to make a significant difference to my calculation. But congestion wise, it's a nightmare because, talking to the taxi drivers, it is clear that don't always get return fares.
In the past there was a coach service and I used it. The times didn't always work (it ran about once an hour) and traffic delays could be an issue but, given the fact that a stop was only 10 minutes walk from home and it's no great walk from the bus station at LHR to T1, 2 or 3 it was totally feasible (T4 was a different issue).
If a railway link was built I would expect to use it provided:
1) They didn't make the fares as stupid as HeX
2) There was a train about every 20 minutes
3) The service operated from about 0500 to 0100 every single day.
4) I don't have to change (well, all right, if I do have to change then I don't want to have to climb stairs (with baggage), escalators, lifts and the like are fine) and I don't want to wait at the change point more than 5 minutes.)