A French government minister has sparked a row by suggesting his country could end UK border controls in Calais if Britain leaves the EU.
Emmanuel Macron told the Financial Times his country could also limit access to the single market and try to tempt London's bankers to relocate.
His comments come as David Cameron and Francois Hollande prepare for security and migration talks in France.
Leave campaigners dismissed the comments as "scaremongering".Conservative MP Bernard Jenkin said "propaganda" was "being produced by other European governments at the request of the prime minister to try to scare people away from voting to leave".
He added: "We pay a great deal of money into the EU and it subsidises a great deal of French farming. Surprise surprise, they don't want us to leave the EU.
"But this is a choice for the British people, not for the French government, and actually we're being asked to believe all sorts of ludicrous things."
Conservative MP Peter Bone, of the Grassroots Out campaign, said: "If asylum seekers start arriving at Dover, we will send them straight back. As an independent nation, outside of the EU, we will control our own borders whether the French government likes it or not."
The agreement between France and the UK that allows the UK to conduct border controls on the French side of the Channel is a bilateral treaty that is not connected to Britain's EU membership.
It is meant to stop people from travelling across the Channel without their immigration status being checked - but has led to the establishment of the so-called Jungle camp in Calais, where about 4,000 migrants are thought to be waiting to cross.
On Monday, there were clashes as French demolition teams dismantled huts in the Jungle.
France could opt to end the border treaty any time - but the country's interior minister Bernard Cazenouve has said to do so would be "foolhardy" and cause "a humanitarian disaster".
His colleague, economy minister Emmanuel Macron, gave a different view in his FT interview, saying of Britain's EU membership: "The day this relationship unravels, migrants will no longer be in Calais."
It follows hotly disputed claims by Prime Minister David Cameron that migrant camps could move to England if the UK left the EU.
Conservative MP Damian Green, a Remain campaigner, told BBC News "it has been very good of the French to let us to put our border controls in Calais" when "the main benefit comes to this country".
And he said voters should take seriously threats by a French minister to scrap the agreement if Britain "tears up" its EU membership.
