Among those in the firing line to make a £17m Hampshire County Council budget cut are Elson, in Gosport, Lee-on-the-Solent, Emsworth, and Horndean.
Council chiefs are taking aim at the ‘least efficient’ in its portfolio
Last year, more than 162,000 people visited these four libraries.
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An alternative to closure of the four, plus six others, would see a reduction of opening hours by a quarter.
The cuts could leave the equivalent of 41 full-time staff members without a job if the 10 libraries shut.
The council said 46 would go if the option to reduce hours is taken instead.
Staff across the service are at risk, due to librarians and other workers rotating between sites.
Now as a public consultation is launched a senior opposition councillor warned ‘it seems no library is safe from closure or cuts’.
The situation is ‘devastating,’ according to the Liberal Democrat libraries spokesman, and Gosport representative, Councillor Peter Chegwyn.
He said: ‘Closing 14 of the 52 public libraries in Hampshire, over a quarter, sounds the death knell for the library service in Hampshire - and the cuts don’t stop there.
‘The previous executive member for culture & communities, Cllr Andrew Gibson, pledged that no library would be closed while he remained in post – and he kept his promise.
‘But now he’s been replaced by Cllr Sean Woodward it seems no library is safe from closure or cuts to services and opening hours.’
The libraries earmarked for closure chosen due to usage, building accessibility, and community need in deprived areas.
The council identified libraries in Bridgemary, Leigh Park and Havant, Stubbington, and Bishop’s Waltham as being at risk given these criteria.
But they were excluded from the closure proposal because of unique circumstances, ranging from high levels of deprivation to community need in a rural location.
The others named in the list of 10 and currently at risk are Fair Oak, Blackfield and Lyndhurst in the New Forest, Odiham, and South Ham and Chineham in Basingstoke.
Employee pay was the biggest expenditure for the library service last year – accounting for more than £8m, or 61 per cent of outgoings. This compares with 11 per cent spent on books.
A further four libraries, which are community managed and staffed by volunteers, could also be shut as the council will be withdrawing support, saving £49,000.
Members of the public are being invited to provide feedback that could lead to a compromise between the two options.
It has been suggested should rally around the community libraries in a show of strength to make a case for them to stay open.
Executive member for recreation and leisure, Cllr Woodward, said the authority would be looking at closing at libraries that were duplicating services regardless of budget cuts
He said: ‘If central government gave us a couple of million pounds for library services we would be still reviewing our library services.
‘There are some libraries in sad buildings, not being well used, and we would look at those.
‘We do need to look at our library service.’
Borrowing of printed books from county libraries have gone from 6.8m in 2009/10 to fewer than five million in 2018/19. The borrowing of eBooks has increased by 62 per cent between 2016 and 2019.
But Cllr Woodward admitted the scale and impact of the changes would not be as great had central government provided more funding.
He said: ‘Would we be doing in on this scale if funding from government was intact? No, we would not.
‘We do need to plug the funding gap.’
The £1.7m needed in savings represented ‘a significant’ part of the library services budget, he said.
Cllr Woodward said: ‘This represents 16 per cent of the overall budget for the service.
‘This still means that a budget of £10m would remain.
‘The proposals in the consultation have been carefully thought through and offer a genuine choice.’
The cuts are part of a bid to make up an £80m shortfall in the council’s 2021 budget.
Wider measures could see people paying for previously-free services, and support for people with learning disabilities reduced.
Cllr Keith House, Liberal Democrat opposition party leader, warned the cuts could keep coming.
He said: ‘The council’s budget isn’t sustainable, and it’s the fault of central government.
‘I think the situation will get worse with Boris Johnson planning to spend money in the north of England rather than the south.
While the library cuts plans were ‘full of detail,’ Cllr House said they were lacking innovative ideas, such as helping the community take over smaller libraries.
He said: ‘It’s particularly disappointing they are cutting support to community libraries.
‘The disadvantage of Hampshire County Council is that it covers a large area and it looks for large solutions.’
Councillors have said it is important for people to contribute to the consultation.
Cllr Woodward said: ‘If the public has better ideas, we would love to hear them.’
All feedback, even to express concern, was needed, according to Cllr Chegwyn.
He said: ‘We urge the 200,000 Hampshire residents who use their local libraries on a regular basis to make their views known and fight to keep all of Hampshire’s libraries open.’
The consultation closes on March 18. Cllr Woodward will make a decision in the summer, with changes implemented in the autumn.
Complete the consultation at hants.gov.uk/library-consultation or pick one up from a county library.