OMG, I went to Cambridge! OK, here's what to do. Take the train from Cambridge to King's Cross, then get on the Tube and go to Trafalger Sq. Go to the National Gallery, see Nelson's Column, maybe take a peek in the Portrait Gallery or St. Martin's-in-the-Field.
Now, shopping or more sight seeing? If the weather is decent, hop on the Tube again and go to Tower Hill and see the Tower of London and take a Beefeater's tour (make sure to tip). If not, go the other direction and get off at High Street Kensington or Notting Hill and shop. Also Oxford St has many shops but more expensive.
If you are into Museums, then try the V&A (Victoria and Albert). It is fabulous and rarely crowded or the British Museum and see the Rosetta stone.
London is my favorite city in the world (and living in Chicago that is saying something). The transportation is easy and affordable and people are friendly and will help if you need it. I never took a tour bus, but that is me. I know that lots of people love the buses so if you want a good overview, go for it!
Oh, now I am "homesick"! I am taking DD in the summer of 2009 for Cambridge's 800th anniversary and I can't wait! Have a wonderful day!