Heathrow Airports own info which I guess must be out of date (although it does say 2007)
http://www.airwise.com/airports/europe/LHR/LHRexpress1.html

Local private car taxis will do fixed price at £30. A friend tool one just last Thursday evening. About half the black cab price.
Problem is they dont like doing the return unless it coincides with a fare into London. Also, they cant use the taxi lane on the motorway so you will sit in traffic. I guess you get what you pay for

If I ever needed to use the train it is half price with my Virgin Frequent Flyer gold card but that doesnt help you much