Six in ten schools across England will be unable to meet the demand for pupil places this year, new data suggests.
A survey, by school-leadership organisation The Key, found that 59 per cent of schools said they had received more applications for places than they were able to accommodate this academic year.
The results came as Labour released an analysis of official data showing that 15 per cent of secondaries are at or over capacity.
The party says that, with more than 300,000 extra secondary pupils projected by 2020, the number of ‘titan’ secondaries with more than 1,600 pupils will need to increase by 72 to 274.
This would include a rise in the number of titans with more than 2,000 pupils - from 27 to 44 secondaries.
Meanwhile the Local Government Association (LGA), has called for local authorities to be given the power to open new maintained schools, or to compel existing academies to expand until every child has a place.
The news comes as thousands of children across the country wait to find out on Tuesday where they will go to secondary school.
On Friday, TES reported that the rise in pupils meant that more secondary school catchment areas are shrinking to less than a kilometre.
The Key survey showed that four in 10 schools had received more than 50 per cent more applications than they had available places. And in one in 10 schools, there were two applicants to every place.
The pressure for places is highest among primaries where 60 per cent of heads said that their schools were oversubscribed.
But more than half – 52 per cent – of secondary heads also said that they were unable to meet demand for places.
The Key's data, based on a survey of 1,188 school leaders, reveals that 86 per cent of schools that faced excessive demand for places lack the money or facilities to cater for the numbers of pupils who want to attend.
Lack of space for additional buildings (25 per cent), insufficient budget (22 per cent) and lack of suitable buildings (19 per cent) were cited as the main obstacles to meeting this demand.
London has the highest proportion of oversubscribed schools – 69 per cent – compared with 52 per cent in South-West England, the survey suggested.
The Department for Education says an average of more than 3,000 secondary school places a month have been created since September 2015.
Schools minister, Nick Gibb, said: “We want every parent to be able to send their children to a good local school. Despite rising pupil numbers the vast majority of parents are able to do so.”
But Labour’s shadow education secretary, Lucy Powell, said: “The Tories’ free market approach to providing new school places just isn’t working and is creating a crisis in school places.”
Labour’s analysis of the number of new titan schools needed was based on the projected need for 303,000 additional secondary places by 2020 and distributing them equally across existing schools.
Roy Perry, of the LGA, said that councils had a statutory duty to ensure that every child has a school place. “If academies are not willing to expand, then powers to create new schools should be returned to local authorities themselves,” he said.
Christine Blower, general secretary of the National Union of Teachers, said: “It is quite clear that local authorities need to be given the ability and adequate funding to open new schools.
“Failure to do this will result in yet more chaos, children being taught in portakabins, larger class sizes and many having to take places in schools away from their neighbourhood.”
Leora Cruddas, of the Association of School and College Leaders, said that additional places could not be created overnight.
“Providing more school places is not just about quantity,” she said. “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.”