Lorry traffic in Dover has increased by a third in the past five years, the port authorities have said, fuelling fears over potential gridlock in the Kent town after Brexit.

The port handled a record 2.6m lorries in 2017, according to its chief executive, Tim Waggott, with annual traffic figures for Eurotunnel, out on Thursday, expected to show a further 1.6m trucks using the rail shuttle to and from the continent.

Port and freight chiefs said the figures underline the need to have a deal in place to ensure freight checks do not hold up traffic at the port.

“The ease with which vehicles and their loads can pass through Dover and the French ports will be a big test of the post-Brexit arrangement,” said James Hookham, the deputy chief executive of the Freight Transport Association (FTA).

He called on the government to make the free flow of traffic through Dover a “top priority” for 2018.

For the first time Calais port chiefs have also joined the public fight for a frictionless border. Jean-Marc Puissesseau, president-general manager of Port Boulogne Calais, said it had record traffic of 2m lorries last year. “It is essential for the Port of Calais and its hinterland that this traffic flow is maintained,” he said.

The FTA and local businesses have previously warned of Brexit chaos with queues of up to 30 miles stretching back towards London if lorries have to be checked for the standard of goods.

The new figures showed that Dover handles up to 17% of the UK’s entire trade in goods worth up to an estimated £122bn last year.

With the town hemmed in by the famous white cliffs of Dover, more checks will cause major disruption not just to traffic, but to the supply chains for everything from food to the motor industry, business warned.

Honda UK said it relied on 350 trucks a day arriving from Europe to keep its giant Swindon factory operating, with just an hour’s worth of parts being held on the production line.

Nissan in Newcastle keeps just half a day’s worth of parts in its warehouses as part of a long-established just-in-time production process and the company fears any disruption to that supply chain will increase costs to manufacturing and the consumer.

“With Brexit talks about to move on to trade, it is essential that all sides commit to the right solution to ensure fluidity at Dover … Jobs and livelihoods depend on it,” said Waggott.

Last year the chief executive of HMRC, Jon Thompson, warned that it could take between five and seven years to get a new streamlined system to deal with imports and exports in place.

The British Chambers of Commerce on Tuesday called on the government to minimise customs administration at Dover.