I just returned from a trip to Budapest. On my way there I had one of those horrible layovers in Heathrow. My flight arrived at about 10pm and the one out was at 8am.
I tried the "Yotel" which is located in Heathrow Terminal 4. These are loosely based on Japanese Capsule hotels (which are about coffin size!), but much bigger.
My room (deluxe) was about 100 square feet, but had a very comfortable bed, nice tv, and a bathroom with toilet, sink, and shower.
Advantages--right in the airport, and there is a free train that goes between terminals. Also, clean and comfortable.
Negatives--they are SMALL! However, I am 6'6" and I managed just fine. Also, if you expect a traditional hotel with sitting area, etc., this is not the choice for you.
Anyway, if you are stuck in Heathrow this may be a nice option. I got 6 very good hours of sleep I would not have had otherwise, and a very nice hot shower.....which the people on my next flight probably appreciated a lot!