My flight goes out of Heathrow but I don't want to stay in London as London is so very expensive for what you get. I don't mind paying $150 for a really nice room, but $150 in London gets you a scary, not quite clean room in a questionable part of town.

I found a room at the University of London in Surrey and almost booked it until I saw the "notice" about how it was on the 5th floor and no elevator.
uh.....no. Not with a full suitcase.