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Normal services have been suspended at Leith, Oxgangs, Sighthill and Newington libraries while the buildings are used to offer PCR tests to people with symptoms of the virus.
Residents in Oxgangs last week called for their library – one of the busiest in the city – to reopen as soon as possible. It has been shut for nearly two years, first due to lockdown, then repairs and now because it is a test centre.
The council announced a few days ago that library services in Leith would be relocated to Fort community centre as a temporary measure, but no alternative has been provided in the other areas.
Councillor Day said he had decided to write formally to chief executive Andrew Kerr after previously seeking a commitment that the libraries would reopen early in the new year.
He said: “We want our libraries back – they belong to the people of Edinburgh, people want to use them and we need the government to find alternative locations for the test centres.
"If they need alternative venues we can try and help find them, but we need the libraries open. They have been closed for far too long.”
He said most of the symptomatic testing centres across the city were temporary pop-up centres in car parks.
“Oxgangs library needs to reopen, but if they want to put a pop-up centre in the car park of Oxgangs community centre we're more than happy to work with them on that. Or there's a big Tesco nearby where they could put a drive-thru centre as they’ve done in other shopping centres.
“We're not saying no to centres, we're saying we need our libraries back in operation and we'll absolutely help ensure there's a continuation of the test centres at another venue.
“There are also a number of NHS clinics and doctors' surgeries across the city where I'm fairly sure we could use their car parks.“We can’t continue to use the council's libraries when people are crying out for them. Many people use them for bus passes, to collect hearing aids, to use computers to apply for jobs – and all that has just been stopped in these locations.”
He also questioned whether PCR test centres were still needed on the same scale now that more emphasis was being placed on people using lateral flow tests.
Both UK and Scottish governments are involved in provision of the test centres.
In his letter to Mr Kerr, Councillor Day says: “I ask that you now write to the UK and Scottish governments, advising them that whilst we remain fully supportive of the vaccine and test programs, we require the use of these libraries returned for public use with immediate effect.
"We should of course offer to support the UK and Scottish governments with alternative sites where and when required.
"I would ask this is taken forward as a matter of urgency and I look forward to a plan of action.