Leave campaigners have seized on new figures from the Department for Education which warn that the number of applications for school places is continuing to rise, while fewer students are able to get their first choices.
Figures from the DfE show that 84.1 per cent of children were allocated places at their first choice for in 2016, down from 86.7 per cent in 2013.
In London, the proportion of applicants getting their first choice dropped to 68.8 per cent.
Similarly, the total number of applicants has risen by almost 10 per cent from 499,968 in 2013 to 548,006 in 2016.
Figures from the Office for National Statistics last week showed record net migration of 333,000, and employment minister Priti Patel said the DfE figures illustrate the impact increasing of immigration on public services.
“‘The shortage of school places - with one in six children in England missing out on a place at their top choice of secondary school - is yet another example of how uncontrolled migration is putting unsustainable pressures on our public services.
“Education is one of the most important things that Government delivers, and it's deeply regrettable that so many families and young people have been let down in this way,” Patel said.
"The truth is that for as long as we remain a member of the EU we are completely unable to control the numbers of people coming to this country - and with another five countries in the pipeline to join the EU, including Turkey, Serbia and Albania, the problem can only get worse.”
However, Labour's Christ Bryant hit back, arguing that economists have forecast the impact of a Brexit vote on the UK's funding for public services would be negative.
“This is more fantasy economics from Vote leave, who are promising to spend money like a drunken sailor when it simply doesn’t exist,” Bryant said.
“The consensus amongst experts is that that quitting Europe would wreck the economy, leading to a £40bn black hole in the budget and big spending cuts for our public service.”