Buzzpat:
Do what LUV-Sled recommend. Oooo, that sounds... ;-)
Consider taking the Express train from LHR to Paddington Station. Non-stop, unlike the Tube, which has many, plus YOU can ask for the travel industry discount...with your airline ID. (For you only, unless your wife has on too.)
Anyhow, look into going to Windsor Castle; walk where the royals have/do and see where many are buried. At St Paul's, try climbing to the top of the dome. Great view, and it shouldn't be too hot that time of very.
Have Fun, and CHEERS!
DFW
P.S. If you're into James Bond and martinis, look into Dukes Bar, near St. James Palace; Ian Fleming was a frequent patron, and coined "Shaken, not stirred" while there.