A dramatic rise in demand could see some parts of England with nearly twice as many pupils as available primary school places in two years, council leaders have warned.
As many as two in three councils could see more children looking to start primary school in their area by September 2016 than there are currently places for, the Local Government Association (LGA) said.
Schools are already having to convert non-classroom space, such as music rooms and libraries, into classrooms and others have been forced to reduce playground space or expand class sizes, the association warned.
David Simmonds, chairman of the LGA's children and young people board, warned of a "desperate" shortage of school places.
"Mums and dads quite rightly expect their child to have access to a place in good school, that is nearby, and in a good state of repair," he said. "But councils are facing unprecedented pressures in tackling the desperate shortage of new school places.
"Councils across the country have been increasing places by expanding schools where possible through additional classes or new buildings. However, without enough resource to provide places we are seeing some schools having to take extreme measures including converting non-classroom space and reducing playground space."
The warning comes as the Government announces 93 new free schools opening across the country, creating an extra 43,000 spaces for primary and secondary school children. But the LGA is calling for the Department for Education to work more closely with local councils so planning for emerging demand for places can be better managed.
Education Secretary Michael Gove told the BBC that the coalition Government had "taken swift action to repair the damage" caused by Labour.
"We have more than doubled funding for new school places and we are also setting up great new free schools, which are giving parents a choice of high quality school places in areas Labour neglected," he said. "Ed Miliband is too weak to apologise for the shortage of school places his government left behind and too weak to stand up to the unions and back free schools."
Speaking on BBC Breakfast, Mr Gove said: "The LGA are quite right that we do have a challenge because the population has been growing for several years now. We warned the last government that we needed to invest more money in new school places and new schools. They didn't at the time take the action that was required so we had quite a lot of catching up to do when we took office. We have done that, we have spent £5 billion which is a huge amount of money, making up for the shortfall that the last government created and free schools are part of that. Free schools are a way of meeting parental demand not just for school places but for high quality school places as well."