Since we're talking LHR, there are no courtesey hotel shuttles. They have been replaced many moons ago by the "Hotel Hoppa" (GBP 3.00 ow, i.e. just 80p less expensive than an adult single on the tube to Piccadilly (or anywhere in Zones 1 to 6, for that matter - a single to Earls Court, Zone 2, is only GBP 2.40).
Beware, the Hotel Hoppa only runs until 11:30pm or so, as Yours Truly has had to find out recently
As for restaurants "on site", there's pretty few places open after 11pm - the Food Village (Terminal 3 arrivals), and a coffee shop (Starbucks? Costa? Caffé Uno?) in Terminal 2. Not sure about Terminals 1 & 4.
Conclusion: Others have said before, try not to get stuck at LHR. If you can't work around it, and prefer a hotel bed to the floor of the landside dep lounge, you might as well look for a hotel in town. Lots of things to do there
There is the LHR Hilton connected by a walkway to LHR T4 then the free HEX to T123
just take the HEX to Paddington ( lots of hotels there) and with a journey time of 15-20mins not too much longer than probably waiting for the Hoppa( or the free local buses to Bath road for the Ren/Marriott/skyline etc)
I had no idea that Heathrow was not a 24/7 Airport like for example Schiphol - do they really boot you out if your flight gets in late evening and you need to catch the next one really early morning....
....by the time you have gone through the whole baggage/security/checkin/security bull-merde then got to a hotel & checked in/check out etc, you spend about 3-4 hours max in the room, and at London prices I object to paying as much for so little time (2-3hrs) asleep.
Seems the object of the exercise is not to get stuck at Heathrow.
PS. Someone told me the other day there was actually a Hotel Airside in Schiphol for just the occasion I mention above, but I didnt see any signs for it over the weekend.
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.
PAXboy Transit passengers will find somewhere to spend the night @ LHR. I've seen the Food Village (T 3) open very late and very early, BAA website claims it's 24/7, dunno if that's true. Not that the Food Village was my idea of the ideal place for a good night's sleep.
Here are some more "sleepover" reports - beware, most of the info is pre-"war on terror".
I've stayed at the Park Inn (formerly Le Meridien) on the north side of the airport -- the free bus stops about 100m from the hotel. It's a nice hotel; the rooms are of good quality, and are reasonably quiet too. At times I've found internet rates for £65-70, although on average they tend to be a bit higher.
Or, pay the £3 Hotel Hoppa fee each way and stay at the Ibis (around £45), Holiday Inn (around £50), or other lower-cost hotels nearby.