How old are they ?
Is a visit to London going to be a 'one off' or rare trip, or do you go there regularly?
When we went, when my dc were younger, we did a lot of walking. Went and saw the outside of all the buildings you see on the TV - Houses of Parliament, Westminster Abby, St Pauls, Marble Arch, Buckingham Palace and the Mews, Downing Street (though that is disappointing now you can't go into it), Horseguard's Parade, Trafalgar Square, some of the main bridges, London Eye.
Another trip we went to the Tower of London (2 for 1 with train tickets, or free with Blue Peter Badge), and saw the crown jewels, and crossed the bridge there and walked along the South Bank - saw the cathedral, the ships, The Globe, the Tate Modern, etc.
Doesn't cost anything, but every time something is on the news, or a royal occasion, they go "Oh, look, we were there"
Mine also liked going up The Monument (close to the Tower) - you get quite a good view from the top, it doesn't cost much, and is right by where the Fire of London started, and they all studied the Fire of London in Junior school.