I've slept at LHR overnight a couple of times. If I landed there in the middle of the night (usually from elsewhere in Europe), I'd just snooze in the middle of one of those airline ticket counters that sits out in the middle of the terminal. They were boxed-in and quiet. Usually I was out of there early the next morning - before the agents showed up to start working flights.

Only reason I did it was the fact that I was living in Wales and the next train was in the morning. Figured there was no point in taking a late-night cab to a crappy airport hotel when I was just going to get up 4 hours later to start traveling again.

This was 1993. I imagine security chases off backpackers snoozing behind airport check-in counters these days.