People smugglers are telling migrants that they must enter the UK before "the borders shut properly" after Brexit, a BBC South East investigation found.
More than 100 people, the majority claiming to be Iranian, have entered British waters in boats this month.
An undercover reporter found smuggling operations were being organised at makeshift camps in northern France.
Authorities said they wanted to stop a repeat of the Mediterranean crisis in which 2,000 migrants drowned this year.
"When [the] UK is out of Europe, the borders will be shut properly," a smuggler told an undercover reporter posing as an Iranian migrant at a camp in Dunkirk.