I used to stay at HGI T2/T3, but honestly HGI by Hatton Cross is better bang for the money (of the two), by far. Free tube to/from the airport, arguably better view because you can actually catch planes on final approach, or getting ready to take off.

I had a 630am flight out of T5 last week. Took the 5am tube, again at no cost, and still had plenty of time for breakfast at the lounge before boarding at 550am.