Yup, heathrow express is good too, still lots cheaper than a cab or taxi and you dont stand the risk of getting stuck on the chiswick flyover for an hour in a cab. A cab from heathrow to say Tower bridge is going to take about an hour traffic permitting.
http://bit.ly/QA1E8P
You can talk an easy stroll from the house of parliament (great late night bar) along the embankment, see the london eye from across the thames, up past 10, downing st (our president lives there) onto trafalgar square, then down the mall to Buckingham Palace in just 30 mins. Longer if you stop off for some brass rubbing along the way (quaint english tradition of rubbing beeswax on a prostitute).
http://bit.ly/Twpxed
what day are you arriving?