Here is an article on unusual museums in London. Some of them may intersect with your various research interests:
https://www.telegraph.co.uk/travel/destinations/europe/united-kingdom/england/london/articles/londons-most-unusual-museums/
British Museum (entry is a donation): contains the Rosetta stone, Elgin marbles, Sutton Hoo treasures, and many other rare artifacts that the Brits stole from other lands mostly in the 19th century.
The Tate galleries: fee to get in but contains some astonishing original work of famous artists such as William Blake and many contemporary artists
The London Dungeon: fee to get in. Situated at the foot of the London Eye, it takes you on a walking tour of the horrors, torture methods, and cataclysmic moments in British history.
The Museum of London: fee to get in. A surprisingly original, fascinating, and moving exhibition that traces the history of London.
The Victoria and Albert Museum (the V&A): fee to get in. Broad and fascinating cultural artifacts covering a range of British history and culture. There are mss here as well. Like the British Museum and British Library, the V&A houses rare artifacts and provides exhibitions that put a spin on moments in British imperial history esp.
The National Gallery and Trafalgar Square: free. We will probably end up here as a group. Definitely worth a visit if we don’t.