Downing Street has confirmed that Prime Minister David Cameron believes that a huge influx of asylum-seekers would suddenly move to Britain if the UK votes to leave the EU.
"We currently have these juxtaposed controls with France. Should the UK leave the European Union, there is no guarantee that the controls will remain in place," the Prime Minister's spokesman said this morning.
"If those controls were not in place, then there would be no stopping thousands of people coming across the channel overnight, arriving in Kent and claiming asylum.
"The camp, and the people in the camp, would effectively move overnight to the south east of England."
Under current rules, the UK government is allowed to conduct border controls at French rather than UK borders, meaning it patrols for migrants stowing away on lorries or trains in Calais, not Dover.
The spokesman's statement followed a report in the Telegraph earlier this morning that Cameron was getting ready to warn that Brexit could lead to tens of thousands of asylum-seekers in the "Jungle" camp in Calais moving across the Channel to Kent.
Former UK Border Authority (UKBA) chief executive Rob Whiteman told the Telegraph the post-Brexit influx could exceed 50,000 migrants per year.
Downing Street's warning is just the latest indication that Cameron will focus on national security as he seeks to persuade voters to back the UK staying in the EU.
But eurosceptics strongly rejected that message this morning, with former defence secretary Liam Fox saying he was "sad and disappointed to see our Prime Minister stoop to this level of scaremongering, especially as he knows the Calais agreement is nothing to do with the EU and agreed between the two governments".
Steven Woolfe, Ukip's migration spokesman, said Number 10's warning was "based on fear, negativity and a falsehood".