In my experience, the only way to avoide the transport costs at LHR is to stay at the LHR Hilton adjacent to Terminal 4. This hotel is generally overpriced, but you can get reasonable deals at weekends.

The Hoopa shuttle was put in place by the airport authority to stop the congestion caused by the masses of hotel shuttle busses. So you pay for the service and a range of busses take you hotels in an specific area. It does work ok, but you do need to pay for it.

Using a taxi to a LHR hotel will not bring a smile from the taxi driver, but London cabbies are generally very professional and, altough steaming about the short fare and the long wait to get it, will take you. But unless you have 4 people together, it will probably be cheaper to use the hoppa service.