The Feminist Library - based at St George's Circus - has launched an emergency appeal to raise funds to stave off the threat of eviction by Southwark Council.
The building is now owned by Southwark Council, and faced with funding cuts the local authority is seeking to increase the amount of rent generated by its premises.
A petition calling on the council to 'save the library from eviction' has now received more than 3,000 signatures.
Based at St George's Circus since 1987, the Feminist Library collection includes more than 7,000 books, 1500 periodical titles from around the world, archives of feminist individuals and organisations, pamphlets, papers, posters, and ephemera.
"As a Southwark resident I've been devastated to hear that we might be soon losing this unique cultural organisation," said local resident Minna Haukka.
"The Feminist Library is just what we need to hold on to in the Elephant & Castle area right now; a place that brings together women from all backgrounds and of all ages.
"It's not only a valuable historical archive – it's a very much alive and passionate community that Southwark should support and be proud of."
Dr Laura Schwartz, associate professor of modern British history at the University of Warwick, said: "The Feminist Library is a wonderful cultural resource that needs to be defended at all costs. Generations of my students have used it for their academic research.
Cllr Michael Situ, Southwark's cabinet member for communities and safety, said: "For the past seven years the Feminist Library hasn't paid any rent for their premises.
"Whilst we recognise and appreciate the fantastic work done by the library, we have a very clear duty to ensure our assets are being managed responsibly and fairly, and that we are being fair to other tenants who are paying open market rent.
"We have offered the Feminist Library a new lease with rent levels that reflect what other organisations in the building are paying.
"We have also given the library the time to find alternative premises, and will continue to help them find an alternative location if we can, but we are unable to subsidise their rent."