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.
"This jungle will be cleared. They will put everyone in jail."
An Afghan, who gave his name as Farhad, told the BBC that he was part of a failed attempt to enter the UK on board a dinghy with 11 others.
"There is a rush," he said. "Everyone is talking about it saying we need to get in quick in case the security gets tighter."
The UK is scheduled to leave the EU on 29 March 2019.
A smuggler, who said he had been a fisherman in Iran, was filmed by a hidden camera planning a crossing.
"A boat, it'll cost you £3,000 to £4,000," he said. "I am taking three people with me, they pay in cash. We get a boat and off we go."
British and French authorities have said the rise in crossings is the result of "organised criminality" and "mafia networks".
Migrants told the BBC they had paid £6,000 each for their place on a dinghy.
They were told that crossing the Channel would be like playing a computer game.
"This part of the journey is like defeating the last monster, it is hard, very hard," the undercover reporter was told.
Officials on both sides of the Channel have warned of the dangers of crossing through the world's busiest shipping lane - a journey that police have likened to trying to "cross the M25 at rush-hour on foot".
Not all boats that depart succeed in reaching the UK, and at least 30 migrants have been intercepted in French waters since 23 November.
Pierre Henri Dumont, a Les Républicains politician in Calais, said migrants were "risking their lives every night here in Calais".
"We need to face the truth," he said "The truth is, we cannot stop everyone."
The Home Office said that Immigration Enforcement and Border Force were "identifying and dismantling the organised crime groups that facilitate illegal immigration".