I originally started this thread, and really appreciated everyone's help. The trip was great, though there was a lot of rain! In the end, I did some street shooting, but most of the stuff that's turning out more interesting was from a couple of night excursions along the Thames: Parliament, Big Ben, Eye in the Sky, lighted bridges. As mentioned above, Trafalgar Square was indeed a mess, hard to shoot anything without getting signs of major construction upheaval.
For some reason, London seems to have been unusually crowded this year end, so there were people coming out of the woodwork!
I would have loved getting out in the countryside, but the closest thing to that I did was go to Hampton Court Palace, a royal residence about 1 hr by Tube and train from central London. Tudor architecture, funky wine cellar, etc. The grounds were interesting, but I was there too late in the day to have sufficient light.