I always pop into Daunt Books and London Review Bookshop when in London.

I also like Libreria, Word on the Water, Primrose Hill Books, Belgravia Books, Lutyens and Rubinstein, Nomad Books, Hatchards, and Walden.

British Library, of course. The book selection at the Tate used to be great too. Also, the National Poetry Library, though small, is worth a visit.

You might also find these links useful, three listicles and a (somewhat dated but still helpful) article about indie bookshops.

https://theculturetrip.com/europe/united-kingdom/england/london/articles/how-londons-independent-bookshops-are-shaping-its-literary-culture/ (Oct 2019)

https://theculturetrip.com/europe/united-kingdom/england/london/articles/the-7-best-second-hand-bookshops-in-london/ (March 2021)

https://www.timeout.com/london/books/londons-best-bookshops (June 2022)

https://secretldn.com/london-bookshops-beautiful/ (Jan 2023)