I'd second (or is thet 3rd ot 4th?) a visit to Windsor even for just a wander for some fresh air
OP and his good lady have plenty of time to get there, have a wander and get back for some lounge time.
If Windsor seems too far away then the tube to Hounslow would suffice even if just for a walk aroudd the park near the tube station and a bite to eat.
All this on the assumption the OP arrives at a tourist suitable time. If they land at 6AM then the airport is the best place to be!