Holidaymakers from the UK hoping to travel to France have endured a third day of disruption as traffic chaos turned the Eurotunnel into a “hotspot of holiday hell”.

Drivers were stuck for several hours on roads around Folkestone after the M20 was turned into a “lorry park” due to Operation Brock, the system designed to relieve congestion at busy times.

Transport experts said the traffic management system – introduced during Brexit – was causing “massive disruption” and urged the government to come up with a long-term solution.

Steve Gooding, the director of the RAC Foundation, said: “It’s high time we replaced the sticking plaster with a resilient solution worthy of the name.”

Authorities in Dover declared a critical incident as holidaymakers reported waiting as long as 21 hours to reach the ports. Volunteers were drafted in to hand out emergency supplies such as food and water to weary travellers.

The disruption sparked a war of words across the Channel as British authorities accused their French counterparts of not sufficiently staffing the border, while Calais politicians blamed Brexit for the additional checks.

Problems on the roads appear to have exacerbated delays at the border. A bad road collision on the M20 on Friday caused long tailbacks near the ports, while Operation Brock created bumper-to-bumper jams on local roads.

Jack Cousens, the head of roads policy for the AA, said on Sunday that drivers were waiting for several hours in traffic before reaching the Eurotunnel. He added: “Dover has now recovered, but Folkestone has become the hotspot of holiday hell.

Andrew Dyer-Smith and his family, who were heading to France for their summer holiday, spent 21 hours in traffic on roads around Folkestone. “We arrived at Folkestone at 9am [on Saturday] morning for a train at 10.30 and then have been slowly crawling along for the last 21-plus hours,” he told the BBC.

Natalie Chapman, from the haulier group Logistics UK, said some lorry drivers had waited to cross the Channel for “well over 18 hours” in queues with no toilet facilities.

The Port of Dover said it had processed 72,000 passengers – more than 200 miles of tourist and freight traffic – since Friday. Its partners worked around the clock, it said, to clear “huge volumes” of vehicles overnight on Saturday.

It added: “We should not have been in this situation in the first place, however.”

Doug Bannister, the Port of Dover’s chief executive, previously blamed French border control officials, Police aux Frontières, for failing to provide sufficient numbers to staff the passport booths – an accusation denied by the French.

Only four of nine booths for the French border controls for travellers leaving the UK were reported to have been staffed on Friday morning, which port officials say led to the backlogs.

On Sunday, Bannister thanked travellers and the town’s residents for their understanding “during this challenging period”.

He added: “I am incredibly grateful to everyone who has turned this situation around, from the French and UK authorities to our ferry operators, Kent partners and our own port staff.”