One of the most magical libraries in London is the British Library within which you can find many encrusted books, old books, new books, maps, collections, scrolls and more. Below is a photo, stolen from google, which is one of my favourite places in this labyrinth of knowledge. To the right of the image is the cafe and restaurant floors where it is perfectly acceptable to get a coffee and study and to the left is a glass cube which you can walk around all four sides (outside the glass) and see some of the oldest collections which the library has. These books have to be requested at the desk and the librarians then retrieve them. The books face out toward you and the librarians have a system on the inside for selecting them. It is pretty magical to see a book get sucked inwards when they are retrieved, or so I would imagine. It is something I always looked for but sadly never witnessed.
Regardless of whether you share my love of libraries if you ever visit London town I would recommend a visit here. They usually have really interesting temporary exhibitions (at the moment there is one on Harry Potter), the building itself is architecturally very interesting (it extends 5 floors underground for enough room to store books and even then has another offsite storage facility). If you are interested in this I suggest you check out the miniature replica on the second floor, and finally the cafe has one of the best chocolate cakes in central London (the restaurant is ok as well but I wouldn’t visit just for that). There is also a really cool optical illusion in the basement close to the coat check… but I think I’ll let you discover what that is if you ever visit.