“The day this relationship unravels, migrants will no longer be in Calais,” he said.
Current regulations mean that entry to the UK can be refused before entering the Channel Tunnel or boarding ferries, rather than once passengers exit on British soil the other side.
It enables lorries to be searched and scanned for stowaways, with any migrants found arrested or removed from the area by police and drivers fined.
Moving the Border Force checks to the UK could mean that refugees would be the other side of the Channel before being discovered, giving them the right to apply for asylum and stay in the country until a decision is made.
Around 4,000 migrants and refugees are currently living in a camp known as the “Jungle” in Calais, with more in Dunkirk, all trying to reach England.
French authorities are gradually demolishing hundreds of tents and shacks, claiming they have sufficient accommodation to rehome migrants in other areas of the country, but activists claim they have underestimated numbers and will leave thousands without shelter and even more desperate to leave.
David Cameron was accused of “scaremongering” when he claimed that a Brexit could see the camps move to Britain last month.
The Vote Leave campaign group said Downing Street’s warning that the French would “love to pull out” of the 2003 treaty had “no grounding in reality”, while Eurosceptic Tory MP David Davis branded the prospect “preposterous”.
At the time, the French interior ministry pointed to a statement by interior minister Bernard Cazeneuve saying there were "no plans" to change the agreement, which was drawn up as part of a bilateral treaty.
Sir Peter Ricketts, the former UK ambassador to France and national security advisor, warned that the French government was under pressure from opposition parties to scrap it.
“If the context changed and Britain made a major decision to leave the EU I think it’s highly likely France would review its position too," he told BBC Radio 4.
Downing Street said the Prime Minister and François Hollande were expected to discuss the situation in Calais at the Anglo-French summit today.
Mr Cameron is expected to make a joint announcement with French President in Amiens on security and other benefits of remaining within the EU.
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