Philippe Mignonet told BBC Radio 4’s Today that the number of migrants smuggling themselves into Dover on lorries would be “even worse” than now.
Around 56,000 attempts by migrants and refugees to get to Kent from France were thwarted by UK border police in 2016, the last time records were available.
“With the custom controls and custom clearances, we estimate that it could bring about 15 mile queues on the motorway 24 hours a day, seven days a week,” Mr Mignonet said. “So you can imagine that a lot of migrants will try to get in the trucks. So yes, it will be even worse.”
His comments came in response to questions about the prospects of Britain leaving the customs union - an arrangement which allows goods to cross borders of European Union (EU) countries without being taxed.
In 2016, the first ever quantitative survey at a refugee camp in Calais found that 82 per cent of its 6,000 residents were aiming to reach Britain.
Many were hoping to join their family or seek work and were prepared to take risks to the enter the UK despite other being hit by trains or drowning during attempts to get into the country.
A Treasury spokesperson told The Independent: “Our aim is for trade with the EU to be as frictionless as possible and we will ensure that any new arrangements do not undermine safety and security at the border."
But earlier this month Michel Barnier, the European Commission’s chief Brexit negotiator, warned if Britain does leave the customs union and single market, "barriers to trade in goods and services are unavoidable".
However, Brexit Secretary David Davies subsequently said that Britain wanted a trade deal with the EU that gives it free, unrestricted access to markets but where it was “not required to obey European rules”.
Before the UK voted to leave the EU, Mr Mignonet warned France would “have to cancel” agreements that sees Britain allowed to conduct border patrols in the country.
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