Southwark Council will investigate the use of volunteers to enable John Harvard Library to open on Sundays if the borough's library review is approved by councillors next week.
After five months of consultation the council has decided not to close any of the borough's twelve libraries, but it will save £120,000 through a "staff reorganisation will be undertaken to rationalise the number of posts at all levels and to deliver a more cost effective service".
Under the proposals, East Street Library will open at 2pm instead of the current 10am on Mondays and Tuesdays. The Library is currently closed on Fridays but will in future be open 2pm-7pm.
The council will recruit volunteers to help keep smaller libraries like East Street open to make a saving of £40,000 a year across the borough. But the report warns that "if the scheme cannot be made to work there will have to be further reductions in opening hours".
John Harvard Library in Borough High Street will see its current hours maintained. The council's consultation revealed a strong demand for Sunday opening, and the review recommends that the use of volunteers is investigated to enable this to happen.
"Libraries are a vital part of the community and a key service for our residents," says Cllr Veronica Ward, cabinet member for culture, leisure, sport and the Olympics.
"They support learning and opportunity, open doors to work, are about enjoyment, information finding, thinking and reading. In short, they help people realise their potential.
"This report shows a great way forward for the borough and unlike other authorities up and down the country, we are continuing to invest in our libraries. The phenomenal response we had from our library users during the consultation period showed just how dear libraries are to the hearts of our residents, and closing any would have been hugely regrettable.
"By finding these savings, and exploring new ways of operating our libraries, we are extremely pleased to be able to keep them all open. This positive step forward, together with the opening of our flagship Canada Water library next month, truly is a cause for celebration."
The review is lukewarm about the options for generating cash from libraries through commercial services such as coffee shops.
The report notes that "procuring a suitable provider for the John Harvard Library cafe has proved to be a challenge, with two different providers having taken on the running of the space and having withdrawn due to being unable to make sufficient income."
Meanwhile Lambeth Council's libraries commission is still working on its proposals for that borough's libraries. Waterloo Library, based in a temporary building in Lower Marsh, will be vulnerable to cuts or closure. Lambeth's cabinet will receive a report from the commission on 21 November.