Library Hub Discover will find you books in other libraries in the UK (plus Dublin).
Library Hub Discover does not tell you which of the libraries it lists you can access. For this info see:
MA students can join Senate House Library, which offers access to these databases, from within the building only:
For other libraries, see:
The Bishopsgate Institute has a library and archive that 'holds one of the most extensive collections on LGBTQ+ history, politics and culture in the UK.' The collection includes books, magazines and archival items.
The Tate Library has produced a guide, Queering the library, to relevant books and other material in its collection.
WorldCat will find you books in other libraries worldwide. Coverage is uneven; e.g. there are some major African cities with no libraries included.
The SIA librarians will help you find books and access libraries anywhere in the world: though please note our knowledge of many countries is limited.