Cockermouth Town Council has no plans to change the opening hours at the town's library following its takeover.
The council was asked by Workington MP Sue Hayman to consider staying open an hour later one day a week, until 5pm, to allow children who did not have appropriate facilites at home to do their homework.
Councillor Eric Nicholson said: "We have just taken this service on and I think we should see how things go in the next 12 months. If there is a massive upsurge in the number of people using the library we can look into opening hours again.
"The library is busiest in the morning, the county council is happy with the hours we are providing. There have been no requests from library users to extend them."
Councillor Alan Smith said: "The library needs stability at the moment, we don't need a kneejerk reaction."
The town council took over the library from the county council in May.
Mrs Hayman wrote to the town council highlighting two issues which were raised at a recent Friends of Cockermouth Library meeting which she attended.
She said the friends were keen for the library to open until 5pm one day a week.
"This would allow children who do not have the facilities at home due to lack of broadband or a suitable quiet space to come along to the library to do their homework," said Mrs Hayman.
She asked whether the council would consider trailing closing one hour earlier, at 3pm, one day and staying open an extra hour on another day.
Mrs Hayman added that the friends group would like to see a stair lift reinstalled at the library.
She said: "I appreciate it is very early days for the town council to be running the library but wanted to offer my help and support if appropriate to enable this to happen."
Councillors felt that a stair lift was not feasible under building regulations.
Councillor Nicholson said: "The stair is the main means of escape in a fire. A stair lift would impede that.
"The message has not got through that it's a big risk for the town council taking this on, the library's future is far more secure now."
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here