pressure’

That figure includes children who moved to Britain with their parents and those who were born here after one or both parents migrated to the UK from their home countries.

The number of school-aged children arriving in the UK from Europe reached a record 25,000 in a single year, the research also showed.An influx of this size would require the equivalent of about 27 new average-sized secondary schools – or 100 primary schools – to be built to cope with the rise in demand for places.

Of those school-aged children arriving in Britain, the highest number came from Poland, followed by Germany and Lithuania, while other eastern European countries such as Slovakia and Latvia also accounted for large numbers of pupils.

Politicians campaigning for the UK to leave the European Union in the referendum next month warned that the increase in the number of children was making it harder for parents to find school places and pushing up the size of classes.

Priti Patel, the employment minister and a member of the Leave campaign, warned it would get worse, with  countries including Turkey “in the pipeline” to join the EU.

“These figures show how the EU’s open borders policies, and the uncontrolled immigration that stems from that, is leading to huge and unsustainable pressures on our schools,” Ms Patel said.

“This is undermining efforts by local councils to ensure they keep class sizes down, and provide school places for all children in their communities.”

The official estimates emerged at a critical time in the battle over Britain’s future in Europe, with the referendum campaign about to enter an intense final six weeks.

David Cameron and George Osborne are expected to step up their warnings about the impact of Brexit on jobs, mortgages and the wider economy, while Leave campaigners will highlight the dangers of uncontrolled migration for schools and hospitals.

The latest government figures, released by the Government’s chief statistician, John Pullinger, were published without fanfare last week on Parliament’s website, on a page listing papers deposited in the House of Commons library. It follows a row last month when ministers were attacked for refusing to publish an investigation into the impact of migration on state schools until after the referendum.

More than a year ago, Nicky Morgan, the Education Secretary, launched a major government review into the issue, and promised before the election to provide extra help for teachers who have to cope with new pupils who do not speak English.

However, the Telegraph disclosed in April that Mrs Morgan would not publish the findings of the report until after the referendum on June 23 at the soonest, and may not publish them at all.Analysts at the Department for Education have been working with government statisticians to map the impact of migration on schools – and the latest figures are likely to have been examined by Mrs Morgan’s officials.

No figures were released showing which areas in the UK were under greatest pressure to accommodate these migrants.

The figures showed that at a time when the UK’s school-age population shrank slightly from 10.5 million in 2007 to 10.4 million, the number of children aged between five and 18 with at least one European parent more than doubled.

The latest figures, for 2015, suggest that there are now at least two pupils in a typical state school class who have parents who are European migrants.

Last year saw the biggest rise in the number of school-aged children from European migrants’ families, when the number increased from 565,000 in 2014 to 699,000 in 2015.

Separate government figures  in the research showed that 123,000 European children migrated into the UK in the past 10 years.

The highest number was again in the most recent year – with 25,000 school-aged children arriving in 2014, when restrictions were lifted on the numbers of Romanians and Bulgarians who could move to Britain.

A government spokesman said: “Damaging our economy by leaving the EU is not the way to control immigration – a damaged and weaker economy would mean less money to spend on our schools.

“This leap into the dark would lead to fewer school places and bigger class sizes with our children paying the price. By building a stronger economy, we will deliver 600,000 more school places over the next five years.”

On Monday the Prime Minister and Boris Johnson will both make speeches setting out their rival cases in the EU referendum. Mr Cameron will seek to make the “patriotic” case for staying in the EU, arguing that Britain must still be “a friend and protector” to weaker European countries.

Mr Johnson will use his speech to attack the idea that the EU single market has been a force for good, in his biggest intervention in the referendum debate so far.