Try the LHR Marriott or LHR Ren on Bath Rd. The latter has been recently renovated. Both have their ExecLounges open 7 days. The Marriott has a decent pool and steam room. What I usually do for an early flight the next day is grab one of the free buses leaving the airport to the hotel and sometimes take the Hoppa back the next morning, since it will stop at the terminals rather than the central bus station. Here's a good map with the stops.
LHR Bus Routes & Hotels

The Marriot thread here has a few discussions on both hotels. You can try here for a start:
Marriott-Family Hotels London

And here is the LHR-specific thread:
Marriott-Family LHR