The Jewish-founded research library, the Warburg Institute, says it is under threat from the University of London - which signed a trust deed in 1944 agreeing to protect the institute.
The Warburg contains more than 350,000 books, including extremely rare volumes and a photography collection.
It now fears it may lose its independence after the university raised its rent by £500,000 - more than quadruple the fee in 2007. Staff believe that the university wishes to absorb the collection into its own main library.
Librarian Professor Jill Kraye said: "This trust deed is a legal document. It is not outdated - Magna Carta was signed in 1215. We want to preserve the unique character and traditions of our library but the punitive costs mean we cannot afford to do so."