My grandparents will travel to London to stay with relatives for a few months, and plan to borrow books from the local (and NOT university) libraries.
1) Am I right that each borough has its own library? See the map below.
2) If the answer to 1 is 'yes', where can I find a website that lists ALL the borough's libraries' websites, instead of Googling each borough?
4) Can books be transferred between libraries of different boroughs? For example, if City's libraries do not have a book, but Westminster borough's libraries do, can Westminster Borough's libaries loan it interlibrarially to City's libraries?
Although I grasp that anybody with proof of UK address is not confined to his/her borough's libraries and can register with any borough's libraries, it is much easier for my grandparents to request interlibrary loans instead of registering with and then travelling to 6 boroughs' libraries depending on which has the book.
Afterword: After the answer below taught me about the London Library Consortium (or LLC), I found a better map under that shows all the London boroughs, plus highlights the libraries in the consortium. This signposts all the individual libraries in the LLC.