Children could be left without school places if councils are not given more powers to deal with increasing demand, town hall bosses have warned.
The Local Government Association has issued a fresh call for authorities to be handed the ability to open new secondary schools, or force academies - which are not under council control - to expand.
Without these powers, councils will not be able to meet their legal duty to ensure every child has a school place, it said.
The warning comes as a poll suggests more than half of secondaries have received more applications this year than they have places available.
Primary schools in England have been struggling to keep up with demand in recent years due to a rising population, and this is moving through into secondary schools.
The Government has said it pumped £5 billion into creating half a million new places over the last parliament and has committed a further £7 billion over the next six years.
Around half a million 11-year-olds across England are due to find out which secondary school they will be attending this autumn.
Last year, around one in six did not get a spot at their first choice.
The LGA said academies now make up round 60% of secondary schools, and if they do not agree to expand, and councils are not allowed to open new schools in areas with a need for places, their ability to provide enough places could be at risk.
Councils have to plan for a 20% increase in secondary school pupils by 2024, when almost 3.3 million places will be needed, the LGA claimed.
Roy Perry, chairman of the LGA's children and young people board, said: "Councils have a statutory duty to ensure every child has a school place available to them but find themselves in the difficult position of not being able to ensure schools, including academies, expand. Finding suitable sponsors with the capacity to take on the running of a successful new school is also proving a challenge.
"Councils have already created an extra 300,000 primary places, but those children will soon need to move up to secondary schools. Councils will do everything they can to rise to the challenge of ensuring no child goes without a place, but all schools must play their part too. If academies are not willing to expand, then powers to create new schools should be returned to local authorities themselves if they are unable to secure high quality free school sponsors in their communities."
In a survey of 1,188 school leaders, conducted by The Key, 59% said they had received more applications for this autumn than they are able to take.
Around 86% said they would find it difficult to meet the extra demand, citing reasons such as insufficient budget and lack of space.
Leora Cruddas, director of policy at the Association of School and College Leaders, said that meeting the need for new school places is "challenging and complex", with some areas lacking space to build.
"Providing more school places is not just about quantity it is also about quality. This means having sufficient resources. Unfortunately, schools are facing a double-whammy of real-terms funding cuts and a teacher recruitment crisis. Existing and new places must be accompanied by sufficient funding and teacher supply."
A Department for Education spokeswoman said: "Instead of scaremongering, the LGA needs to ensure they use the funds provided by Government to secure enough places.
"Councils are responsible for ensuring there are sufficient school places in their area, and we expect them to plan effectively and make good investment decisions. This requires certainty, which is why funding is allocated three and a half years in advance of places being needed - giving councils time to plan while still allowing the flexibility needed to make adjustments should local circumstances change.
"Where local authorities identify the need for a new school they are required by law to invite proposals to run a new free school and then forward these to the department to decide who would be best placed to do this."