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London 4 day itinerary? - british war museum

I'm happy about going to London, and I plan a route. I already have a list of all the places I want to go and are grouped by their proximity to each other, but I'm not sure how much you can fit in four days. Feel free to add, what do you think you should go to start, or anything that is not important.

London Eye
Westminster Abbey, Parliament, Cabinet War Rooms
British Museum
Trafalgar Square, National Portrait Gallery, National Gallery
Regent's Park
Natural History Museum, Victoria and Albert Museum
Tower of London, Tower Bridge
Imperial War Museum
Globe Theater
St. Paul's Cathedral
Hampstead
Buckingham Palace, the Changing of the Guard
Day trip to Oxford or Cambridge (or both?)
Windsor Castle, perhaps, but Oxford and Cambridge have priority