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A French minister's comment that Paris would no longer stop migrants from crossing the Channel if Britain left the European Union won a sceptical response from pro-Brexit campaigners Thursday.

It accompanied comments from French President Francois Hollande who warned of "consequences" in the British people vote to leave the union in June's referendum.

It comes as French police moved in to close down parts of Calais' "Jungle Camp", leaving migrants' huts burned to the group and refugees fleeing to other parts of the camp.

In an interview with the Financial Times, French Economy Minister Emmanuel Macron said a so-called Brexit could scupper an agreement that allows Britain to conduct border controls in Calais.

"The day this relationship unravels, migrants will no longer be in Calais," he said, echoing UK government warnings that a vote to leave the European Union in the 23 June referendum could result in thousands arriving on England's shores overnight.

Hollande on Thursday warned that there would be "consequences" for how migration was managed after meeting Prime Minister David Cameron for an Anglo-French summit in northern France.

"I don't want to scare you but to tell the truth, there will be consequences... including on the question of people... the way in which we manage migration issues," he told reporters.

Under the 2003 Le Touquet border treaty, the UK is allowed to carry out border checks on French soil, stopping many migrants.

But those pushing for the UK to leave the bloc reacted with scepticism to Macron's comments, noting they contradicted the official position of the French government.

Last month, French Interior Minister Bernard Cazeneuve dismissed the idea of ripping up the Le Touquet treaty, saying it would give a green light to people smugglers and would only boost the numbers trying to cross.

"That is the genuine line to take from the French government," Conservative lawmaker Bernard Jenkin from the Vote Leave campaign told the BBC on Thursday.

"What we are having now is propaganda being produced by other European governments at the request of the prime minister to try to scare people (out of) voting Leave."

Cameron's official spokeswoman said the government had not been aware what Macron was going to say until his comments appeared in print.

France has been a destination for thousands of refugees fleeing war and poverty in South Asia, Africa and the Middle East. Many have headed to Calais and made temporary homes in the Jungle Camp.

Many have used France as a staging post to reach the UK, often via a precarious route through the Channel Tunnel on the back of lorries.