Town hall bosses have been warned not to let a plan to outsource library services "erode" the service.
Wandsworth Council, in partnership with Croydon Council, has embarked on a plan to hand the running of the borough's libraries to an outside body.
Last week, the Tory-led council in Croydon voted in favour of the scheme, which drew criticism from Labour councillors.
Wandsworth's Labour Group has since raised fears about the plan.
Councillor Leonie Cooper, its environment, culture and community safety spokeswoman, and the GLA candidate for Wandsworth and Merton, said: "Although the Labour Group is happy to support an exploration of new ways to cut costs from our library system, it's vital that any outsourcing does not lead to an erosion of services, or any further reductions to library opening hours or supplies of books."
She said any change must "protect the low-cost access to computers and the internet, as well as maintain up to date stocks of books for both children and adults. It's also crucial that we continue to preserve spaces for people to work, read and study".
Coun Cooper added: "Finally, if the Council is to look at partnering with others boroughs, it should open discussions with numerous local authorities, to ensure we end up with the very best deal for the residents of Wandsworth.
"To date, it would seem that discussions have centred around one individual borough."
The council's existing in-house library team is expected prepare a bid to continue running the service.
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