There are a myriad of things to do in London. You must add these to your list:
See a play in the West End. Check out Time Out London. Make sure you check out the The National Theatre as well. The Royal Shakespeare Company, RSC, also has a London season.
Buckingham Palace and Changing of the Guard: Make sure to see the State rooms at the Palace if they are doing tours when you are there. They are open usually late July through early October. After seeing the wedding, I remember my first trip to the Royal Mews on Buckingham Palace Road. Make sure you go if you want to see the carriages used in the wedding and processions.
Check out the recent growth in Leicester Square and walk through St. James. Check out the schedule and catch a noontime or evening concert at Wren’s St. James Piccadilly.
In the City of London, see St. Paul’s and the other Wren churches. If you can get in to see Wren’s model in the Library of St. Paul’s, you will love it. St. Paul’s also has some wonderful music programs. You can find some wonderful old pubs to have lunch throughout the City.
In Westminster, visit Westminster Abbey, see Big Ben and Parliament. If you want to see Parliament in action, you can attend some sessions or take a tour.
In Whitehall, visit the Cabinet War Rooms which I understand have recently been expanded. The architect Indigo Jones’s Banqueting House is great to visit. It is a Palladian inspired building with a Rubens painted ceiling from 1636.
Continue on to Trafalgar Square and walk through St. Martin-in-the-Fields. The church has chamber music programs and also jazz concerts. Move on then to Covent Garden and The Market with its many wine bars and restaurants.
Take a walking tour. There are a number offered where you join a group at a certain Underground Station. I did a great one of Dicken’s London with stops at locations mentioned in his books.
As far as museums go, visit the National Gallery and the British Museum. On my last trip, I really enjoyed the Courtauld Institute Galleries which contains the private collection of Samuel Courtauld. There are works by Manet, Degas, Gauguin, Van Gogh, Seurat and Cezanne plus others by Rubens, Michelangelo, Leonardo, Durer and Rembrandt.
The Tate Britain, in Westminster, is also a must. Then there is the newer Tate Modern which houses the contemporary collection in a renovated Bankside Power Station.
Next to the Tate Modern is the Shakespeare’s Globe Theater. The theater was built and opened in 1997 as a replica of the old Globe theater where Shakespeare’s plays were performed. I happened to catch Vanessa Redgrave in the Tempest. The season runs from Late April through August. Plans are underway to build an indoor theater as well.
Explore Knightsbridge and Belgravia. I love the architecture on the old squares like Cadogan Square and Belgrave Square.
In Kensington, visit Kensington Palace and Victoria and Albert Museum if you love furniture, porcelain, textiles, tapestries, jewelry glass, Medieval, Gothic, Renaissance art as well as Asian and Islamic art. I have never been to either the Palace or the Museum but hope to visit both on my next trip.
Millennium Bridge: Make sure to see this contemporary bridge opened in 2001. If you are traveling with children you might take a boat trip on the Thames, visit the Tower of London and Tower Bridge and visit the London Eye, the large Ferris Wheel.
Royal Albert Hall: This is a great venue to catch a performance, concert or the BBC Proms in the Summer.
A great way to see the city is on a bike or walking tour. Fat Tire Tours, a popular operator, has a number of bike tours, walking tours, a pub tour with beer tasting.