Some councils will be forced to increase primary school capacity by as much as 20 per cent within just four years to avoid a major admissions crisis.
An official Whitehall analysis shows that areas including London, Bristol, Coventry, Leicester, Luton and Plymouth are facing the biggest squeezes on places.
The projections suggest local authorities need to expand primary school places by between 10 and 20 per cent by 2014 to meet the extra demand.
Four councils in the south east – Slough, Wokingham and the London boroughs of Lewisham and Barking and Dagenham – face the biggest pupil population rises of more than 20 per cent.
The disclosure is made in an internal report by Partnerships for Schools, the Government’s school buildings quango.
Rising demand for primary school places has been put down to a surge in the birthrate combined with an influx of migrants in some areas.
In all, it is believed that an additional 350,000 primary places will be needed over the next four years.
Last night, Government sources claimed Labour had effectively ignored the looming crisis despite repeated warnings by Whitehall officials.
It was claimed that the previous Government lavished billions of pounds of public money on high-profile schemes to reconstruct existing secondary schools – instead of building additional primary school capacity.
The Coalition has already axed Labour’s £55 billion Building Schools for the Future programme which was set to transform England’s secondary schools.
The squeeze on primary places is already biting in some parts of the country, where hundreds of infants are still without reception classes three weeks into the new academic year.
Sarah Teather, the Children’s Minister, said dozens of children did not have places in her north London constituency of Brent.
"It's a problem that's common across London and it's going to get worse,” she said. “It's particularly acute in the primary sector and, of course, as children move through the system, we've got this bulge of children without adequate school places.”
The Whitehall report – obtained by The Daily Telegraph – shows which areas need to build additional primary school places by September 2014.
Seventeen of London’s 33 boroughs must increase primary places by between 10 and 20 per cent, while two face bigger pupil rises of more than a fifth. A further nine are facing smaller increases in pupil numbers of up to five per cent.
Outside the capital, 38 councils face rises, including Coventry, Leicester, Birmingham and Nottingham in the Midlands and large parts of West Yorkshire and Greater Manchester.
Cities in the south west, such as Bristol, Plymouth and Exeter, and counties in the south east, such as Surrey, West Sussex and Hertfordshire, are also likely to experience more pressure on places.
Sir Steve Bullock, Mayor of Lewisham, which is facing one of the biggest shortages, said: "The situation in Lewisham is very serious and will continue to be so until we get additional Government funding to provide more primary places.
"We have opened 18 additional classes on time so that every child due to start reception this year has a place. This was only achieved through the hard work and commitment of Lewisham headteachers and governors.
"The birth rate in Lewisham is now around 4,800 a year and if 80 per cent of these children apply for a place in a Lewisham school, we will have 3,840 applications for 3,156 places each year. This is an unacceptable situation.
"The Government needs to understand the urgency for more primary places and this has to be a priority for the Comprehensive Spending Review. We were in discussion with the previous Government before the election but had not been successful by the time the election was called.”
--By Graeme Paton,25 Sep 2010