Patel, a member of the Vote Leave campaign, said class sizes were already overstretched with an 8% increase over the last year in the number of pupils in classes of more than 30.
The remarks are likely to infuriate both Downing Street and Nicky Morgan, the education secretary, who was forced to counter criticism of the pressure on school places earlier this year by saying the government had created more than 400,000 new ones since May 2010.
“The EU is undemocratic and interferes too much in our daily lives,” Patel will say. “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 £2bn 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.”
Vote Leave said its research showed that one in five primary schoolchildren has a first language other than English and that the UK can expect an additional 261,000 European citizens to be in the UK school system by 2030.
It said this could increase to 571,000 if the “A5” accession countries – Albania, Macedonia, Montenegro, Serbia and Turkey – were to join within that timescale.
David Cameron has repeatedly said Turkey will not join the EU for decades and that he will veto it happening if it were to do so in the next few years.
Patel also put her name to a press release referring to the claim by Cameron’s former director of strategy, Steve Hilton, that the prime minister was told he would not be able to meet his net migration target if Britain remained in the EU.