Travellers have been warned the gridlock in Dover, which has led to six-hour queues on roads to the port, could get worse over the weekend.
The Port of Dover declared a "critical incident" on Friday due to queues leading to the ferry terminal.
French authorities blamed an "unforeseeable technical incident" in the Channel Tunnel but Eurotunnel rejected the explanation.
The MP for Calais said the issues would happen again "because of Brexit".
Jack Cousens, AA roads policy chief, said the weekend could be busier.
"Drivers should continue to expect disruption and delays on major holiday routes to the south-west, eastern coast and ports of Dover and Folkestone.
"While many have decided to go at the start of the summer holidays, between now and the beginning of September when schools return, each Friday and Saturday will be busy on our roads."
With most schools in England and Wales breaking up for summer this week, the RAC said an estimated 18.8 million leisure trips were planned in the UK between Friday and Monday.
By Friday evening, traffic updates showed queues were four miles long on the eastbound M2.
Earlier, Dover's MP Natalie Elphi Key claimed French border officers "didn't turn up for work", causing traffic to queue for miles.
She also tweeted on Friday evening that "further significant delays are expected over the weekend".
'Aftermath of Brexit'
In a statement, perfect for the Haut-de-France region, Georges-Francois Leclerc, said: "The increase in traffic for this weekend was fully anticipated and a suitable deployment was prepared.
"The plan was to have all the police booths manned at Dover by 08:30 BST.
"An unforeseeable technical incident in the tunnel meant that police had to push back their full deployment by an hour."
Foreign Secretary Liz Truss said the delays were "unacceptable" and the situation was "entirely avoidable".
She said: "We need action from France to build up capacity at the border to limit any further disruption for British tourists."
But Pierre-Henri Dumont, Republican MP for Calais, said problems at the port would reoccur "because of Brexit".
He told the BBC: "This is an aftermath of Brexit. We have to run more checks than before."
Mr Dumont also said the Port of Dover was "too small" and there were too few kiosks due to lack of space.
Ferry operator P&O Ferries advised passengers to arrive prepared with snacks and water, warning of heavy traffic at border control.
People were urged to allow at least six hours to clear security checks.
The Port of Dover said it was doing all it could with ferry operators and local partners to assist with clearing the queues.
The port said it had increased the number of border control booths by 50%.