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 It is not outdated - Magna Carta was signed in 1215.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."
The university's Andy Williamson, said: "The University has evolved with the times and is giving consideration to seeking an alteration to the terms of the Trust Deed."
Originally the private library of Jewish art scholar Aby Warburg, the Warburg moved to Bloomsbury in 1934 to escape the Nazi regime.