Wheelchair-bound Carol Buck has been unable to visit her local library since the Mayor of Doncaster, Peter Davies, closed two premises and made cuts to 12 more.
Two thirds of councillors voted in favour of an amendment to allocate extra funding for libraries but Mr Davies refused to budge.
A judicial review into the decision began at Leeds Combined Court Centre last month but Mr Justice Hickinbottom dismissed the application yesterday.
The judge said he appreciated the closures would adversely affect Ms Buck but he could only intervene if the mayor and his cabinet had acted unlawfully and he was satisfied they had not.
“In my judgment they have exercised their functions properly and lawfully and for these reasons I dismiss this application,” he said.
A hearing last week was told how the decision to close two libraries and transfer 12 more to volunteers was made by Mr Davies and his executive last November.
It was raised as a key issue during a council budget meeting, in which 43 councillors voted for an amendment to allocate extra funding to provide at least one member of paid staff in the affected libraries. Only six voted against it and three abstained.
But English Democrat Mr Davies said he was not going to change the budget and the 14 libraries would continue to close or become volunteer-run.
The action has been seen as a challenge to directly-elected mayors’ powers which, if the judge ruled the other way, could have had wide-ranging consequences.
Speaking after yesterday’s judgment, Ms Buck said: “It’s upsetting. I’m disappointed really, but I can’t do anything about it now.”
Supporters will be closely examining the judgment to see if any other legal avenues are open to them, she added.
Mr Davies said he was pleased with the outcome and “delighted with the success” of Doncaster’s community-run libraries.
“This was never a decision that was taken lightly but it was necessary in order to to make the required savings,” he said.
“This case should never have been taken to court and I am furious that this has now cost the taxpayers of Doncaster over £30,000.
“At a time of cutbacks, this is money that could have helped to save jobs.”