An additional 261,000 children from EU countries can be expected to sign up for schools in the UK by 2030 if Britain votes to remain in the 28-nation bloc on Thursday, the Vote Leave campaign has claimed.
And the campaign said the number of additional pupils could swell to 571,000 if all five states which have applied for EU membership - Albania, Macedonia, Montenegro, Serbia and Turkey - join in the near future.
Government minister and Leave campaigner Priti Patel said the demand for more classroom places would put extra pressure on schools which are already "overstretched".
Vote Leave said the increase in school-age European nationals was likely to add between £1 billion to £1.9 billion to the cost of the UK's annual education budget by 2030.
The campaign calculates that between 2000 and 2014, some 152,000 school-age migrants came to the UK from other EU countries.
And it said the numbers are on a "steep upward trajectory", with the 16,200 annual average between 2010 and 2014 almost three times the 5,800 average between 2000 and 2004.
The number of school-age children with one or more parent from a non-UK European nation has more than doubled from 309,000 in 2007 to 699,000, said Vote Leave.
Based on its own estimates of future immigration if the UK remains in the EU, the campaign group calculated that at least a further 261,000 could join the school system over the coming 15 years - or as many as 571,000 if the Union expands.
Ms Patel said: "The EU is undemocratic and interferes too much in our daily lives. We have seen that with the scale of migration, and the impact this has had on local communities - and key public services such as the NHS, housing and schools.
"With more countries waiting to join the EU, including Albania, Serbia, and Turkey - and with British taxpayers paying almost £2 billion to help them join - this problem can only get worse.
"This research proves that class sizes are already overstretched, with an 8% increase over the last year in the number of pupils in classes over 30. These demands will only increase if the UK remains in the EU with no control over its borders.
"Thursday offers a once-in-a-lifetime opportunity to say that the situation is unsustainable - and to recognise that it is hurting British families. On Thursday, we have the chance to take back control and Vote Leave."