There is probably some very good hunting museums to go visit and also some great parks full of deer to go check out if you prefer that type of stuff over the typical tourist destinations.
I remember landing in paris once, getting in cab, seeing the Eiffel Tower from the cab window at a distance and thought cool, lets keep moving, i got a plane to catch at the other airport so i can head south for an alpine hunt in the pyranean ranges...i prefer mountains over tourists every day of the week..
The London Dungeon, the changing of the guard at Buckingham Palace, and the Tower of London Crown Jewels were the most memorable excursions for me while there many years ago.
Stonehenge was cool also but probably too far away for a short visit and they roped off all the stones years ago because the loonies were partying there so you can't go right up to them anymore.
A two-hour double-decker bus tour is a great way to get a quick overview of the city. Relax up top in the open for great views.
If it were me today, I'd try to see an EPL match -- Arsenal, Tottenham, or Chelsea. Or maybe go check out the Wimbledon grounds. Well that's assuming I couldn't line up a date with Kate Beckingsale of course.