Gladstone, the former prime minister of Britain, left his library to the nation. Known as St Deiniol's, it is situated in the small town of Hawarden (pronounced Harden) just outside Chester. Anyone can visit it provided they can demonstrate that they are engaged in research for which the library would be useful. As I recall from my only visit there, the library emphasises theology and British history and all the books are from Gladstone's time, so if you are researching atomic theory, you're out of luck!
I'm very grateful to my friend Peter Wright, of Deeside Films, for supplying us with this footage.