Any London attractions require advance tickets?

Warner Brothers Harry Potter Studios - book yesterday
Churchill War Rooms - book soon

Remember many museums are free in any case.

You are traveling at the height of tourist season. You are traveling to one of the most popular international cities. Covid travel restrictions are over…..crowds will be massive, so, yes pre book “ popular “ sites.

Is this your first time in London? What are you interests?

IMHO you should pre book these sites:
Tower of London
Churchill War Rooms
London Eye
Parliament tour
Tower Bridge Experience
Theatre (Hamilton or Wicked or Mama Mia or Witness for The Prosecution as some examples)

I've booked for a few things in April:

National Gallery After Impressionism: https://www.nationalgallery.org.uk/exhibitions

Queen's Gallery at Buckingham Palace - special exhibition Dressing the Georgians: https://www.rct.uk/collection/themes/exhibitions/style-society-dressing-the-georgians/the-queens-gallery-buckingham

--> I only go to the Queen's Gallery if the exhibition is something that is of interest to me. If this show is not something you'd want to see, skip it, lol! If it is of interest see how the times are booking up for the day you'd want to do it. I am going to see it on a Bank Holiday so I thought it might get booked out and grabbed the time I wanted a couple of weeks ago.

The only other thing I've booked is a musical - The Great British Bake-off - which sounds like fun!

Westminster Abbey is closed when I'm there or I'd book that ahead. I've been to the Churchill War Rooms many times or I would book that ditto the Tower of London.

My usual strategy for museum booking is to watch the calendar dates and see how the bookings are going. TBH, I got kind of skittish about exhibitions getting sold out due to the huge demand for the Vermeer exhibition in Amsterdam. I realize none of the special museum exhibits this year in either Paris or London will be in the same blockbuster status as the Vermeer, but still I let myself get nervous, lol. The things I've booked ahead are all venues I will visit anyway so it doesn't harm to get my tickets in place.

Yes - if you want to see a play at the Globe you must book tickets now. Tickets for museums that charge should be bought in advance - they can book out. If there is a walking tour you want then also book that ahead. If you plan to go to high tea or cream tea in one of the big hotels or places that take reservations, also make those ahead of time. Buckingham Palace, Tower of London, those also come to mind.

While the national art galleries are free, that only applies to their permanent collections. Glamorous special exhibitions often carry a fairly stiff admission and getting tickets in advance can speed up admission.