The Government is currently enforcing full export controls, but import declarations can be deferred until July.
On Thursday Gerald Mayrwöger, business development manager at Vos, said he is still working on customs paperwork for trucks that have been waiting to leave the UK since Tuesday.
He said: “We are very much suffering on the southbound [route] from the UK to the western European Union.”
Trucks leaving the UK have to complete a seven-step process in order to take the ferry or the Eurotunnel.
Mr Mayrwöger said the customs paperwork sometimes takes longer than the lifetime of a 24-hour permit drivers are given to pass through Kent, meaning the company is then fined.
Drivers are also getting lost looking for border offices, Mt Mayrwöger said, then having difficulties with the language barrier when they find them.
He said the company is now planning to reduce the amount of cargo it carries out of the UK due to the disruption, and said: ”It’s really a big, big administration challenge. We simply cannot afford it anymore.”