I frequently stay out at LHR if I'm on an oh-dawn-hundred flight back to the US on United.
I usually get a good rate at the LHR Renaissance. I don't bother w/ the Hoppa. The Ren is the last stop before Heathrow on the free public bus (#105, 140, 285, for example) route, so literally you get on & 5 minutes later get dropped at the airport. Exiting the Ren, turn right & walk about 50 feet to the bus stop.
Cheers.