August 26, 2024 is a Bank Holiday. Will the following attractions be open: British Museum, Westminster Abbey, London Eye, Tower of London, Parliament, Buckingham Palace, Churchill War Rooms?
Most attractions in London are open on Bank Holidays. But it would be a good idea for you to check the website for each individual site you have listed, though, as some may be closed on Mondays generally.
As Mardee said, check the website for each individual site you have listed for current visitor information. Think of the August bank holiday probably being much like Labor Day in the States. Banks may be be closed, some workers may have the day off, and some popular attractions might be a little busier. I've been in London for the August Bank Holiday and as visitor it was no different than any other day.