Academy conversions should be suspended to help councils focus on supporting schools and nurseries to stay open for the children of key workers and vulnerable pupils, according to local authority leaders.
Councils are having to divert their efforts away from co-ordinating school places and organising emergency food supplies amid the Covid-19 crisis, the Local Government Association (LGA) said.
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The warning came ahead of parents finding out whether their child will get their first preference of primary school this autumn, on what is known as National Offer Day.
The LGA has called on the government to temporarily suspend the conversion of maintained state schools to academies so they can prioritise essential work.
Council staff are having to spend time on hundreds of academy conversions, which involve the transfer of staff, assets and financial agreements, according to the LGA, which represents councils across England and Wales.
It said the Department for Education (DfE) should turn its attention to National Offer Day on Thursday and ensure there are enough school places in the autumn amid the Covid-19 disruption.
Judith Blake, chairwoman of the LGA's Children and Young People Board, said: "Councils' number one priority is to help keep schools open and support families in need, including those with vulnerable children on free school meals, at risk of abuse or with disabilities.
"Council staff are working flat out at reduced capacity, and taking council teams away from their primary duty of care to see through applications for academy conversions is clearly not in the interest of either councils or schools during this unprecedented time.
"We want to work with the government to ensure that schools are given the support they need over the immediate term, and this includes urgently placing a temporary pause on academy conversions during this time."
Paul Whiteman, general secretary of the NAHT school leaders' union, said: "Councils, like schools, are operating with limited staff and resources during a very difficult time.
"We agree that only the most urgent and essential work should be going ahead, and everything that can be paused should be."
Sara Ford, deputy director of policy at the Association of School and College Leaders, said: "At this time, we believe that our members should be allowed to focus their attention on delivering the best possible service to the children and young people for whom they are responsible.
"We are also concerned that, given the changed circumstances, sufficient thought needs to be given to the appropriateness of the timing of any proposed conversions, as what children and young people will need most when they transition back to school is a sense of security."
A DfE spokesman said: "In light of the current public health crisis, our priority is the welfare of young people and staff in the education system.
"Ofsted has suspended routine inspections – we will therefore not be issuing new academy orders to schools judged inadequate."