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The Port of Dover has declared a "critical incident" because of long queues leading to the ferry terminal.
Boss Doug Bannister told BBC Radio Kent the port had been "badly let down" by the French border controls.
He said they were "insufficiently resourced" in France and working slower than normal, leading to delays of up to five hours.
National Highways said the weekend was expected to be one of the busiest periods of the year for holidaymakers.
The Port has accused the French authorities of ruining the summer getaway for thousands of families.
Holidaymakers booked on sailings from Dover have reported being stuck in five-hour queues to complete border checks before they can check in for their ferry.
The port said in a statement it had made "significant investment" to increase its capacity, and shared traffic volume forecasts "in granular detail with the French authorities".
The statement continued: "Regrettably, the PAF [police aux frontieres] resource has been insufficient and has fallen far short of what is required to ensure a smooth first weekend of the peak summer getaway period."
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.
That is the most since the company began tracking summer getaway numbers in 2014.
'Zero movement' in Dover
One traveller posted on Twitter: "I'm booked onto 8am ferry from Dover and it's total gridlock. Moved 50 metres per hour.
"At this rate it'll be 34 hours before I get to the port.
"I have a screaming toddler and three-month-old."
Another person attempting to make the Channel crossing said they had been "waiting five hours and still not in the port".
They added: "Sat in lanes waiting to get to border control. Zero movement."
Ferry operator P&O Ferries has advised passengers: "There are currently queues in excess of four hours to reach the border controls.
"Our check-in remains free flowing and once you reach us, we will put you on the first available sailing.
"Please arrive prepared for a prolonged wait. Carry snacks and additional water with you."
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