Just come back from a day tour of London, mainly for the benefit of my girlfriend.
We travelled up by train, then cycled along the old cobbled lanes by the South Bank of the Thames from London Bridge to Westminster Bridge. Hacked our way through the traffic to Buckingham Palace, where the roads are car-free. Cruised up and down the Mall, then across Mayfair (gentlemens clubs and msart tailors), Soho (seedy vice district and trendy media place) and Covent Garden to the British Museum. The new covered courtyard took my breath away, dont miss it. A mummy or 2 later, we head on to St Pauls Cathedral, and head through the empty financial district to buzzing Spitalfield market for a falafel snack, then down to the Tower of London, across Tower Bridge (the one the should have been moved to Arizona!!), then back down the South Bank to the new Tate Modern gallery. Its an aweome place, a vast power station with some fab collections.
Man, MichaelW, that sounds like a wonderful day of bicycling. I can just imagine bicycling around London with my wife checking our Museums and the sights. Wow, what a great day.
I toured around London by foot, taxi, and red bus once. I visited most of the places you mentioned. In retrospect, the tour would have been much more magical and more mysterious if I had been on a bicycle. Why, it would have been a magical mystery tour.