I'd definitely head west (eg Windsor) rather than into central London with that amount of time. Or if not, Kingston or Richmond, all for lunch on the river? If you arrive on time and don't have to worry about luggage, even the most jittery of travellers should have a couple of hours to grab some food/wander around.

Buses would work but unless you know your way around, best book local taxis (NOT black cabs. Windsor/Heathrow should be max £25 each way, suspect Kingston/Richmond would be similar.