Lots of sightseeing today. London Walks, a local tour company, provides many inexpensive and interesting short walking tours to suit almost any taste. Check them out online. No pre-booking necessary, just show up at the proper time and place.
We went on one to the British Museum in the morning, drank beer and ate at the not to be missed and hard to fine "Ye Olde Mitre" pub located down an obscure alley. The tea at harrods, and another walking tour at night of Pubs across the river (South bank).