The boss of the port of Calais has said there could be tailbacks up to 30 miles in all directions and potential food shortages in Britain if a Brexit deal involves mandatory customs and sanitary checks at the French ferry terminal.

Jean-Marc Puissesseau made an impassioned plea to Theresa May and Michel Barnier to put plans in place immediately to avert congestion in Calais and Dover, where bosses have already warned of permanent 20-mile tailbacks.

At the same time a leading politician for the Calais region said the problems in France would be 10 times worse than at the Irish border.

At a private meeting at the European parliament, Xavier Bertrand, a former French health minister and the president of the Hauts-de-France political region, said politicians needed to grasp the magnitude of the problem.

“I know Ireland is going to be a real problem, but please remember the economic issues in Ireland are 10 times smaller than what is going to happen here,” he said. “This is a black scenario, but it is going to get darker and darker,” he said, urging politicians in Brussels and London to take urgent action by setting up working groups and listening to business.

Bertrand angrily denounced those who had power to influence the Brexit outcome. It was not right that economic operators should be expected to “sit on their hands waiting very anxiously for something to happen”.

At the same meeting, Puissesseau said both sides would be affected by the problems at the ports, with suppliers from the UK trying to get their goods through strict EU controls treated no better than those from a developing country.

“The UK is part of the 21st century. But this takes us back 100 years. This is sad,” he said. “From Brexit day, 100% of our traffic will be from outside the EU. I tell you honestly that GB will be a third country, this frightens me. There’s such a long history between the UK and EU.”

His message to May and Barnier was to “be intelligent” on the economy. “At the moment, 70% of food imported comes from the EU. Even if that goes down to 50% after Brexit because of controls, it still needs to flow smoothly; people still need to eat,” he said. “If there are delays it could end up rotting on the side of the road.”

Calais has embarked on a three-year €700m (£625m) expansion plan at the port with new docks to accommodate longer and wider ferries.

“We based our calculation on the growing population in the UK. We thought if there were more and more people, then their needs for food, cars, everything, increases and traffic will increase and we need to prepare for that,” said Puissesseau. “But then Brexit comes along and we have a new problem.

“I’m not sure the two negotiators on both sides of the Channel take into account the important position of Dover and Calais ports.”

At peak, the ports have the capacity to process between 250 and 300 trucks an hour and delays could mean 15-mile tailbacks building up over 10 hours.

He said Calais could return to the havoc of July 2015 when truckers were trapped in their cabs for three days in searing heat with 30-mile queues from Calais to Dunkirk, 25 miles inland to St Omer and 20 miles west to Boulogne. “I am worried about the slowdown of traffic if there are controls. Imagine 2m trucks being controlled in Calais,” he said, in reference to the 4.3m trucks that use the port in both directions a year.

Other big businesses at the meeting, including Mars, DHL and Airbus, echoed the concerns of the French.

DHL said it might look at a new train route from Maidstone and Lille. “We looked at this 20 years ago but did nothing with it, but if we have major problems at the port we will be looking for a solution away from the port,” said Patrick Boone, the head of DHL’s road network, Europe.

Airbus reiterated its threat to leave the UK if it does not get clarity on border arrangements soon.

“We don’t make cheese or lamb,” said Pascal Belmin, the head of EU regulatory affairs at Airbus. “But we have problems too. The wings are made in the UK. We need the parts to flow. Some parts cross the border three times.”

Airbus also needs its staff to be able to move freely around its sites in Europe.

Airbus may leave UK unless there is urgent clarity on Brexit trade Read more

Mars called for continued regulatory alignment and said the cost of divergence in environment and food processing standards could be huge to an industry that generates €1tn in revenue and hundreds of thousands of jobs. “By no means should we create differences,” said Andreas Georg, its strategic sourcing director.

Government data shows that after Brexit, 185,000 traders will be making customs declarations for the first time. “That is a lot of learner drivers, a formidable educational task,” said James Hookham, the deputy chief executive of the Freight Trade Association.