skydriller - This is my understanding, based on reports of people who try to sleep their deliberately. It may be that, if you can show a ticket and boarding card, that they would let you stay. The airport is closed to most flights from 24:00 to 05:00 (varies, I think). There are a certain number of night flights allowed each year but I gather that these are mostly cargo.
I have never had the problem of missing a flight and staying over at Heathrow, as I live in the area! I sit to be corrected on how the staff at the terminals will treat you, particularly if you are a transit pax.