Members of The London Library have access to a unique humanities library for use in their own homes or workplaces, in addition to congenial spaces in which to read and work.
The London Library refers to the people that use it as members. Nice. Its a private library so the mechanism of joining is a bit more explicitly membership-like than how public library patrons (at least in the United States) get library cards.
This label also leads to a great opportunity on library websites: a page detailing the benefits of membership. Here’s one from the London Library.