Figures show almost 800,000 additional children aged 11 or under will be in state education by 2020 because of rising birth rates and the effects of immigration.

According to the Department for Education, the primary population is set to soar by a fifth – reaching its highest level since the early 70s.

The disclosure underlines the crisis facing local authorities in some areas that are being forced to cope with the biggest surge in school applications.

It also prompted fresh claims that Labour ignored repeated warnings over the looming population boom by cutting primary school places.

Local authorities in parts of London, the West Midlands and South West have already been forced to install mobile classrooms and educate children in church halls in recent years because of a shortage of space.

Earlier this month, it emerged that Sutton Council in south London had urged ministers to increase the maximum class size for infants to ease the pressure on schools. It suggested allowing schools to admit 32 pupils aged five to seven into lessons instead of the current limit of 30.

Today, the DfE said it was spending £4bn in areas with the tightest squeeze on places over the next four years to create additional primary school capacity.

But Gavin Williamson, the Conservative MP for South Staffordshire, criticised the last Government for failing to deal with the problem. He obtained data in a Parliamentary question showing that Labour cut funding for primary school places, despite warnings as early as 2007 that demand would rise by 110,000 in six years.

“Labour didn’t just ignore clear warnings of a surge in the primary school population, but they actually went against them – cutting funding for extra school places and ordering councils to cut surplus places,” he said.

“Thanks to Labour’s inaction, thousands of children could have been left without a place in the coming years.”

According to projections published today, there are currently 4,025,000 pupils aged under 11 in state-funded nursery and primary schools.

Numbers are expected to grow year-on-year to 4,824,000 by 2020 – an additional 799,000. It will be the biggest number of pupils in the system since the early-70s.

The rise would be equivalent to around 3,260 average-sized primary schools or an additional 26,600 classes of 30 pupils.

Earlier figures show that some 440,000 primary school places are unfilled nationally – but they are not in the areas expected to face a squeeze.

Despite a declining secondary school population in recent years, figures also show that numbers will start to increase again in 2016 because of the effect of rising birth rates.

In total, the Government estimate that the primary and secondary school population combined will rise by 810,000 by the end of the decade. Around 105,000 of these pupils are believed to be from immigrant families.

Stephen Twigg, Labour’s shadow education secretary, said the latest figures showed the Government neded to “respond to real need in our education system, not just promote pet projects” such as academies and free schools which primarily cater for secondary pupils.

“There is an urgent crisis in our primary school system that the Government is ignoring,” he said. “Ten per cent more places are needed before the election. By contrast, secondary school numbers are expected to be five per cent lower than in 2011.

“The majority of need is for primaries yet half the funding from the Autumn Statement will go on pet projects like free schools.

“Only a third of free schools in the pipeline are primaries, and the areas with the biggest need will not get a free school. This shows how out of touch the Tory-led Government is with real need on the ground.”