4 hour layover at Heathrow - do I have time to leave airport?

No. To get into town is about an hour, and another hour back. You have to be back at the airport two hours ahead of your ongoing flight to get through security again, so that shoots all of your time. Even if everything worked like clockwork and you weren't delayed anywhere, you would have no time to actually see Westminster Abbey once you got there. Even with five hours, it's not very possible.

You've double posted the question. This one's in the Italy forum.