So many wonderful suggestion were given. What can I add?

I strongly! recommend you a visit of Courtlaud Institute gallery - not a big, but a very rich museum of paintings - all paintings are of most famous brushes only! Surprisingly, the museum is not heavily visited. Don't miss it!

Another recommendation- a trip to the Windsor castle with all its splendour. Come before 10 am to see the change of the guard ( the change of the guard can also be seen in Buckingham). Beeing in Windsor visit Eaton College. There are guided tours inside this place where learned many famous British people, include prince William.

Don't miss the great St Paul Cathedral. Tower is a must, as though it has a lot of precious things to see.

If you go to Greenwich, try to do that by boat from near the Parliament.

Being in London, it's a shame not to visit at least one of its beautiful parks - Hyde or Regents. I'd more recommend Hyde with Wellington Museum (with a statue of nude Napoleon) and Kensington Palace where Diana lived.

About musicals, I loved most Phantom of the Opera, Les Miserables !, Miss Saigon and Whistle Down the Wind.

Catch a good view of the city from the Tower bridge or from the nearby Monument.

Sincerely, Alex Elbert Jerusalem Israel