Two Cockermouth mums presented a 442-name petition to the town council, calling for the library to extend its opening hours.
Grace Bennion and Hilary Royston-Bishop handed over the document to mayor David Malloy at a council meeting on Wednesday.
Grace said to members: "Thank you for saving the library, we realise this is a big financial commitment.
"We have had a lot of support from families who want to use the library but currently cannot."
Councillors will discuss the call for library opening hours to be extended at their next meeting, on November 21.
Grace has spoken to lots of people about the campaign, including most of the local head teachers.
"People have been really positive and supportive, lots of people think it's a logical thing to do," she said.
She has two children, Elsie, four, and Bryn, 18 months.
"My daughter loves to read and I love to read with her, to her and with her little brother," said Grace.
"We have always tried to use Cockermouth library as much as possible to get books, but since the library reduced its opening hours to 10am to 4pm during the week and 10am to 2pm on a Saturday we are finding it very difficult to enjoy, or even get the opportunity of using the space.
"During the week, after school, we can just about make it before closing to get some books, but this is a rushed and not enjoyable experience."
Grace and Hilary, who has two young children, would like the hours to be extended on at least one weekday. This would allow them and other parents - including those who have children at outlying village schools - to enjoy what is on offer.
She feels that Saturday visits are not an option for many families because there is so much else going on.
The council took over the Main Street library from the county council last year.
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