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No guarantees have been given by council bosses that all of Kent's libraries will reopen when coronavirus restrictions are eased later this year.
Kent County Council (KCC), which runs library services in 12 districts, excluding Medway, has stopped residents from browsing bookshelves or accessing computers at its 99 sites since the third national lockdown on January 4.
Instead, click and collect services are running at 27 Kent locations.
However, concerns have been raised by county councillors that not all libraries will reopen when the limits on people's lives start to ease in the coming weeks.
Former KCC cabinet member, Cllr Eric Hotson (Ind), of Maidstone Rural South, has sought "assurances" that a library in his division, Marden, which has been closed since the first lockdown on March 23, will not stay shut.
Cllr Hotson, who was deselected from the Conservative party ahead of the May local elections, told a virtual meeting last Thursday: "Now is the time for honesty.
"Can you please confirm that when this awful pandemic fades away that all 99 libraries will reopen and there are no plans to make any closures?"
Five months ago, KCC announced that libraries which had not yet reopened would remain closed until April 2021. This amounted to around 68 in total.
KCC's deputy leader and finance cabinet member Cllr Peter Oakford (Con) was questioned about their uncertain future last week.
On Thursday, he said: "I can't guarantee that 99 libraries are going to reopen in three months time. When the time is right we will start reopening as and when we can."
At last week's KCC budget meeting, where 5% tax rises were agreed, Cllr Hotson was refused a verbal response on "political" grounds.
However, KCC cabinet member for communities, Cllr Mike Hill (Con), who oversees libraries, pledged to provide a written update to him in private.
"We have funds and plans for when we are permitted to start a reopening programme for the libraries."
Libraries were shut in Kent for nearly four months when the first wave of Covid struck the UK in March last year.
Twelve were reopened in July and more followed in August, with additional safety measures in place, including hand sanitiser stations, one-way systems and face mask wearing.
January's lockdown forced their closure to the public for a second time, however coronavirus cases have fallen dramatically over the last six weeks.
Pressed on the reopening, Cllr Oakford said: "Mr Hill has made it clear that he wants to reopen all of the libraries - that KCC can - as soon as possible.
"We have funds and plans for when we are permitted to start a reopening programme for the libraries.
"It takes three months from when we are given the all-clear, due to the preparation work we will have to do."
Any book items on loan before the January lockdown have been extended by KCC until May 31, 2021.