Campaigners are preparing to go to the Court of Appeal after losing their High Court challenge against library cuts.
A judge rejected their claim that decisions to close six "treasured" libraries in Brent, north-west London, were "fundamentally flawed and unlawful".
Local residents fighting the cuts are being backed by celebrities including playwright Alan Bennett, singer Nick Cave and bands Depeche Mode, the Pet Shop Boys and Goldfrapp.
The six facing closure are Kensal Rise, Barham Park, Preston Road and libraries at Neasden, Cricklewood and Tokyngton.
Brent Council says the closures will help to fund improvements to the remaining library service and contribute towards the £104 million of savings it needs to make.
The campaigners accused the council of failing to comply with its statutory duties when it decided in April to close half of its libraries while promising to provide "fewer but better resourced libraries".
But Mr Justice Ouseley, sitting at London's High Court, ruled there was no evidence to support the allegations made against the authority and dismissed the campaigners' application for judicial review.
Asking for permission to apply for permission to appeal, Helen Mountfield QC, appearing for the campaigners, said: "This case is important not only for Brent but for other libraries and public authorities generally." Refusing permission, the judge said: "I do not regard there is any real prospect of success."
Later, campaign group Brent Save Our Six Libraries said they would ask the appeal court itself to hear their case. Margaret Bailey, a children's nursery manager and one of the leaders of the anti-closure campaign, said: "We are obviously disappointed with the decision given by the judge today. We are determined to appeal if allowed to do so."
Brent Council leader Ann John said: "We are pleased that the council has been completely vindicated. The judge, having carefully considered all the complaints, has found in our favour on each and every point. It means that we can now push ahead with our exciting plans to improve Brent's library service and offer a 21st-century service for the benefit of all our residents."