Almost two thirds (61 per cent) of councils fear maintained nurseries in their area will close unless future funding is protected.
And that could mean thousands of children with special educational needs and disabilities (SEND) missing out on the care and support they need, a survey suggests.
Since 2017, the government has provided £55 million each year in supplementary funding for maintained nurseries, of which there are currently 397 in England.
Now according to data from the Local Government Association (LGA), of the 56 councils with maintained nursery schools, 33 per cent said it was very likely they would close without protected funding and 28 per cent said it was fairly likely.
More than half of (52 per cent) said losing funding would result in reduced support for children with SEND, and the same number said it would mean reduced support for disadvantaged children.
The LGA is calling on the government to address the underfunding of SEND provision in next week's Autumn Budget.
Yesterday, MPs heard that some councils were "stringing out" decisions about care plans for children with SEND in order to save money.
Anntoinette Bramble, chair of the LGA's children and young people board, said: "As our survey shows, councils have grave concerns about the future of maintained nursery schools if the current funding does not continue beyond 2020.
"This provision is now under threat unless government commits to an extra year of funding in 2020-21 as part of wider work to find a long-term sustainable funding solution in the Spending Review.
"This is on top of the overarching funding pressures councils are facing in providing support for children with SEND, which we would like to see the chancellor address in next week's Autumn Budget."
Children and families minister Nadhim Zahawi said: "Children with additional needs should have exactly the same access to early education as every other child.
"That is why we are supporting councils and childcare providers to provide the right support for children with SEND through our disability access fund, worth £12.5 million, and the early years national funding formula, which means councils must direct more funding to where need is higher.
"Maintained nursery schools make a valuable contribution to improving the lives of some of our most disadvantaged children, alongside wider government support including our free childcare offer for two-year-olds – that's why we are providing local authorities with around £60 million a year up until 2020 to protect maintained nursery schools funding."
He also urged councils not to make "premature" decisions on the future of these nurseries.
Earlier this month, the minister said he was gathering evidence to back demands he was making for more government funding for maintained nursery schools.