The cost of creating places for the 880,000 extra pupils expected in England’s schools over the next decade could push schools to breaking point, say council leaders.
The Local Government Association fears the crunch on school places could soon reach a tipping point with no more space or money to extend schools.
The LGA wants the government to fully fund the cost of all school places.
Ministers said the last Labour government had failed to plan ahead.
Official government figures, published last year project that by 2023 there will be a total of 8,022,000 pupils in England’s schools - up from 7,143,000 in the current academic year.
The LGA calculates the cost of creating places for all these pupils could be £12bn.
It says the government’s commitment of £7.35bn for extra school places leaves a shortfall.
As well as more central government funding it wants councils to be given the powers to open new schools to meet local need without bureaucratic burdens.
The association’s comments come ahead of Thursday’s deadline for the parents of some 370,000 three and four-year-olds to apply for school places for their children.
It says councils are “pulling out all the stops to ensure there is a place for every child”.
Separate figures from the Labour party suggest one in five primary schools is already over capacity, with more pupils than they have classroom space for.
The party sent Freedom of Information requests to all of England’s 152 local education authorities. 130 replied.
The responses suggest almost one in five primary schools (18%) do not have enough capacity for their pupils, with children in over-large classes or temporary makeshift classrooms.
These include a primary school in Northumberland which is holding classes in a converted double-decker bus and another in Bristol which has taken over an old police station.
More than three quarters (78%) of the councils that responded saw a need for additional primary places in the next three years, with half saying they will need more secondary places.
Cllr David Simmonds, chairman of the LGA’s Children and Young People Board said: “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.
Cllr Simmonds said councils were trying to create places on time and in the right places but were hampered by red tape and lack of money.
“The scale of this crisis is too much for council taxpayers to pay for alone. Additionally, much of the decision making about new school places rests in the hands of the government, whose funding for school places came late. As a consequence, councils are carrying a billion pounds worth of costs which puts pressure on other school services.”
The government has focused funding for new schools on academies and free schools which are independent of local authority control.
Labour says this policy is failing to provide places in areas where they are needed.
The shadow education secretary, Tristram Hunt said: “Parents have a big choice to make at the election in May.
“On education the choice is this: a Labour Party committed to sensible and pragmatic solutions for overcome the growing pressures on school places, or David Cameron’s irresponsible schools policy that prioritises money for new schools in areas with surplus places.”
Conservative Education Minister Nick Gibb blamed the crisis on Labour.
“The last Labour government failed to plan for the future, cutting funding for school places during a baby boom while allowing immigration to get out of control, and they wasted millions of pounds of taxpayers’ money on their failed Building Schools for the Future programme.
“By contrast, because of the tough decisions we have taken as part of our long-term economic plan to get the economy back on track, this government has dealt with an unprecedented increase in demand for school places by protecting the school budget from cuts, investing an extra £5bn to create new school places and spending £18bn to improve school buildings across the country.”