The closest thing you'll get to a hotel would be one of those little wooden ones found in Monopoly sets (and you'll have to carry it along from home).

Arrayed around the perimeter of LHR are a number of doss houses and "hot pillow" hotels serving stranded, delayed and transit pax. They vary in quality, but generally fall into both of two categories, "Spartan" and "over-priced". Apparently, some are served by public transit buses, but only those intimately familiar with routes and schedules should attempt to employ them. Taxis are available, but on my last visit, needing a pillow upon which to rest my head, the driver seemed unable to identify or locate the squalid lodgings I had chosen, until I threatened to beat him about the head and shoulders to prevent him from delivering me to a hotel from which he apparently receives a commission for "Shanghaied" travelers. Many have restaurants, but the quality and variety of cuisine available is comparable to that produced in the galley of the overnight ferry between Palermo and Pantelleria or a Rumanian minesweeper laid up in ordinary in the shipyard in Constanta. Low expectations should be your theme of the day.

Of course you could just stay at the airport (at which, depending on which terminal you're in, a place to sit usually becomes available after a wait of no more than an hour or two. Carry along a video camera, for passing through LHR are enough interesting subjects to fill a documentary entitled "Do These Folks Really Have Homes".