Well...maybe...
But the cheapest lodging in London is still the Heathrow Lodge just down from the Terminal 5 building at Heathrow...
The closest Underground station to Heathrow Lodge is actually the Station inside Terminal 5...
But there is a free "employee" shuttle bus that runs right by the Lodge to the Terminal...and from the Terminal to the Lodge!
A bit far out from the City Center...but the price is right for the budget traveler to London...