hotel/restaurant with shuttle
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
