David Cameron was accused of “desperate scaremongering” after claims that 'Brexit' could lead to thousands of asylum seekers arriving in the UK overnight.

The Prime Minister also claimed that leaving the EU could hamper the UK’s ability to fight terrorism and international crime.

Despite the warnings, No 10 suggested that Mr Cameron still ruled nothing out when it came to the EU.

Campaigners on both sides of the argument accused Mr Cameron of running a ‘Project Fear’ designed to frighten voters into staying in the EU.

Stephen Gethins, the SNP's Europe spokesman, said: “This is exactly the kind of scaremongering that we want to avoid.

"We want to see a positive campaign to keep Scotland in - focused on the benefits rather than these Project Fear tactics.

"The Prime Minister should be more worried about his government’s failure to help ease the European refugee crisis."

Eurosceptic former defence secretary Liam Fox said that he was “sad and disappointed” that Mr Cameron had “stooped to this level of scaremongering”.

Former Tory minister David Davis denounced what he said were "desperate" actions.

Downing Street is keen to counter 'Out' campaign's argument that only by leaving the EU can the UK regain control of its borders.

Mr Cameron said that there was no guarantee that the existing border arrangements would remain after a 'Brexit'.

The UK currently has an agreement to check passports on French soil.

The deal, which led to a dramatic fall in the number of asylum seekers coming to the UK, was struck in the early 2000s.

UK sources suggested that there would be very little reason for France to continue with the current arrangements if the UK was outside the EU.

Mr Cameron said: “If we can... stay in a reformed Europe, you know what you get.

"You know that the borders stay in Calais.

"You know that we have that vital information, whether it's about terrorists or criminals travelling around Europe, because we are part of those organisations."

The Prime Minister’s spokesman said:“There is no guarantee that these controls would remain in place and there would be nothing to stop thousands of people crossing the Channel overnight and arriving in Kent and claiming asylum.

“This is a perfectly feasible scenario that could happen."

Philippe Mignonet, the deputy Mayor of Calais, appeared to agree the French would cancel the treaty.

"We will have to cancel these agreements, because England won't be in Europe anymore," he said. "So that will really be a foreign country for us."

But John Vine, the former chief inspector of UK borders, said: "I don't necessarily think this would collapse overnight. If it didn't exist there would still be border controls."

Meanwhile, it emerged that the UK has boosted its emergency war chest by by £25 billion, amid fears leaving the EU could trigger a collapse in the pound.