dodger21 and I hopped over to Heathrow from Amsterdam for a night to catch a Kings-Ducks season opener few years back, we managed to cover almost everything 'touristic' by speed-walking and using the tubes a lot. We even filmed a documentary
However, the airport itself took about 2 hours to get through if I recall, due to immigration lines being ultra long.
That and by the time night came around we literally couldn't get our legs to work anymore ;p