I have a layover at Heathrow for 6 hours. I am going to leave Heathrow between flights. I'm thinking 1 hour to get out of the airport. 30 minutes Heathrow Express to Paddington. 2 hours walking around London. 3 minutes back to Heathrow with 2 hours to spare. Of course I wish I had more time to spend, but am I crazy, or can this work? Also what should I do for 2 hours in London?
train to Paddington is 15 minutes, though Paddington itself is not the centre of the universe and you might need a further tube trip to somewhere interesting. Yes, you should have time to see, say, the National Gallery or whatever. But make sure how long before your second flight you need to check in.
If you are a nice and lovely looking lady then visit me in those two hours as I am hardly 5 miles from Heathrow, lol
Otherwise depends where you are coming from and if you have visited London before. First of all you should make sure that you do not miss your flight due to this. Then most of the people visit Piccadilly circus, Oxford street, or just go and see Trafalgar square as you only have limited time. But whatever you do, do not go too far away from Paddington as you have to catch train from there. And make sure you know about the timings of the Heathrow Express.
Or how about Hampton Court Palace? http://www.hrp.org.uk/hamptoncourtpalace/
The 111 bus goes from Heathrow Central to Hampton Court. At a guess a 40 min bus ride. The central bus station is adjacent to Terminals 1,2 & 3, but there is a free shuttle bus to it from T4 and T5.
As other users have said, i would definately not risk it.
Many airlines will offload you and your bags if you leave the airside departure lounge in case you dont make it back. Not a problem in itself, but it far increases the chances of your bag not getting on the flight.
Have a meal, buy a good book, find a quiet spot in the terminal and have a sleep!