A “critical incident” has been declared by the Kent port due to six-hour queues, with tourists urged to consider staying away.
Natalie Elphicke, Tory MP for Dover, claimed French border officers “didn’t turn up for work”.
It is one of the busiest periods for foreign travel from the UK as most schools in England and Wales break up for summer this week.
Passengers embarking on cross-Channel sailings from Dover must pass through French border checks before they can board a ferry.
The port said in a statement that it has increased the number of border control booths by 50% and shared traffic volume forecasts “in granular detail” with the French authorities.
It went on: “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.”
Port chief executive Doug Bannister said: “We’ve got a critical incident under way.”
He told BBC Radio Kent: “We’ve been badly let down this morning by the French border.
“Insufficient resources and much slower than then even normal transactions, which is leading to significant congestion around the port this morning.”
He said it will be “a very difficult day” and the situation has been “escalated to the highest levels in our government”.
He added: “I would consider holding off heading for the port at this point in time until more is known.
“It is really difficult to get into town this morning.”
Ms Elphicke said there has been “weeks of preparation” for this week by the Port, the Department for Transport and Kent Resilience Forum, and “much work with French counterparts too”.
She went on: “Despite all this, French border officers didn’t turn up for work at the passport controls as needed. This has caused massive delays.
“More French officers are reported to be arriving. It’s vital that the French passports controls are fully staffed during this peak holiday period.”
Delays at Dover are causing tourist and freight traffic to be stuck on gridlocked roads in the area.
One Twitter user wrote shortly before 7am: “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 said they have been “waiting five hours and still not in the port”, adding: “Sat in lanes waiting to get to border control. Zero movement.”
Ferry operator P&O Ferries told passengers: “Please be aware that there is heavy traffic at border control in the port of Dover.
“If you are booked to travel today please allow at least six hours to clear all security checks.”
Passengers are advised to take additional water and snacks.
The RAC said an estimated 18.8 million leisure trips are planned in the UK between Friday and Monday.
That is the most since the company began tracking summer getaway numbers in 2014.
Transport analytics company Inrix predicted the M25 – London’s orbital motorway – would see some of the worst jams due to the summer getaway, singling out the stretches between Bromley and the Dartford Crossing; Maple Cross and the M3; and the M23 to the M40.
The A303 near Stonehenge in Wiltshire, the M4 between Cardiff and Newport in South Wales, and the M5 south of Bristol were also likely to see queuing traffic.
Fuel price protests in south-west England did not initially cause disruption to drivers.
Avon and Somerset Police said: “A slow-moving protest convoy of about 10 vehicles has joined the M5 northbound at Junction 24 Bridgwater.
“Currently there are no delays on motorways in our area due to protest activity, but some motorists may experience longer journey times today.”