We will be arriving in London on the Eurostar on a Sunday and leaving London early Wednesday morning. Staying near the British Museum. Right not my main concern is what to do that first day. Can't see a play at night since there is no London theater on Sunday night. Don't want to spend the day at the British Museum. Plan on visiting the Tower of London on Monday morning and doing Big Ben, House of Parliament, Westminster Abbey, Buckingham Palace the third day. Other things I would like to see: Harrods, The National Gallery, National Portrait Gallery, London Eye. All suggestions appreciated.

What time do you arrive on Sunday? Harrods is open on Sunday from 11:30 a.m. until 6:00p.m.
It is a huge store with a pretty amazing Food Hall so you could spend a fair bit of time there.

Sounds like you won't have to worry about jet lag so why not see the National Gallery or the National Portrait Gallery, Harrods and the London Eye that day. You might also consider afternoon tea.

I recently had a very nice Sunday evening at Ronnie Scott's jazz club.
They also do a Sunday jazz brunch which always sells out.

Manyt theaters are dark on Sundays, but certainly not all. The situation is VERY different than it used to be.

http://www.westendtheatre.com/catego.../sunday-shows/

See if St. Paul's or Westminster Abbey has evensong on Sunday night.

At least at St. Paul's, Sunday evensong is at 3pm . Not sure about the abbey, but their website will have the info.

How is this for the first day? Trafalgar Square with the National Portrait Gallery and the National Gallery. Then off to Harrods and then Convent Gardens around dinner time. Is Convent Gardens similar to the South Street Seaport in NY but without the water? Also, how would the Lord Mayor's show factor into a day that includes Westminster Abbey, Big Ben and Changing of the Guard? Thank you.