As schools in England face finding places for almost a million additional pupils over the next decade, council leaders have warned there is not enough money or space to expand.
Official figures show that an estimated 900,000 extra pupils will require school places in England by 2023 - a figure that the Local Government Association has warned could leave schools at a "tipping point".
The LGA, which represents local authorities across the country, has estimated the cost of finding these places at £12 billion - £4.65 million less than the figure pledged by the Government so far to create more places.
Around 90,000 places were created in 2012/13 by councils, and more are being established. However, the LGA says the scale of the problem is too big to be solved at a local level.
As well as ensuring school places are fully funded, the Government must enable councils to open new schools according to the needs of the local community, the LGA said.
A surge in pupils - fuelled in part by a rising birth rate - has already put pressure on primary schools, with a Bristol primary last year taking over a converted police station to house extra pupils.
In October, a primary school in Northumberland began teaching pupils in a bus it bought on eBay, after converting the vehicle into classrooms to solve the lack of space.
David Simmonds, chair of the LGA's children and young people board, said: "Mums and dads rightly expect their children to be able to get a school place and councils and schools are doing everything they can to provide this, in some cases going to extraordinary lengths to create places.
"But we fear a tipping point could soon emerge when councils and schools can no longer afford the massive costs for the creation of places, nor find the space necessary for new classes, if this crisis is not properly dealt with."
The LGA's warning comes just days before the January 15 deadline for parents to apply for primary school places for this September.
Around 370,000 three and four-year-olds are estimated to require school places in the autumn.
We do not want any child to be without a place. That is why, at a time when parents are making big decisions about their child's future, we are calling on the Government to commit to funding the creation of school places and hand councils the powers to open new schools, for both primary and secondary-age pupils, before time runs out.
A 2013 National Audit Office study warned that by September 2014 an estimated extra 256,000 primary and secondary school places would be needed to meet demand
in 2014 the Times Educational Supplement concluded that hundreds of thousands of pupils could end up with less room to play outside because a squeeze on school places has meant classrooms are being built on playgrounds and playing fields
Information on school expansions from 82 local authorities suggests that just over a third (35%) of primary schools that have grown or are due to grow in size will end up with less outdoor space for youngsters
Conservative Minister Nick Gibb said that the Government has "dealt with an unprecedented increase in demand for school places".
He said that schools had been protected cuts, have benefited from investment of an extra £5 billion to create new school places and spending of £18 billion to improve school buildings across the country.
"As a result we now have a million more pupils in good or outstanding schools than in 2010," he added.