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Traffic snarl-ups spilling into Dover town have already held up emergency vehicles, disrupted bus services and even stopped carers reaching clients.
Cllr Nigel Collor has questioned the county council cabinet member for transport about how the town can be protected from further disruption post-Brexit.
He says that tourist traffic in the town has to be helped when there are delays as is done for lorries using the main routes, through schemes such as Dover TAP.
Cllr Collor said: "Tourist traffic is extremely important.
"There is more potential for the Dover town area to be well and truly gridlocked as has happened in the past with emergency vehicles unable to get through, bus services disrupted or even cancelled, lifeboat crews being unable to reach their station and, above all, carers not being able to get to their clients to render assistance.
"Plus there is a greater likelihood of needing to provide humanitarian needs for people in queuing cars and coaches."
His statement stressed that there are measures to deal with lorries, such as Dover TAP, Operation Stack and Project Brock, but there is little such provision for tourist traffic.
He asked: "Will the cabinet member for planning, highways and waste advise what measures are being discussed to deal with tourist traffic as part of Brexit preparations?"
Cllr Collor's question was put forward at the full KCC meeting at County Hall, last Thursday .
Cllr Whiting told him multi-agency groups were meeting to prepare for the situation in Dover post-Brexit.
Cllr Collor explained to KentOnline's sister paper, the East Kent Mercury: "I have been lobbying hard in a number of quarters and while it appears that a number of ideas of how to deal with freight traffic are being drawn up there is, as yet, no apparent moves on how to deal with the tourist traffic, cars and coaches.
"If they get delayed for too long humanitarian needs need to be addressed such as water, food and toilets.
"While we all hope that the traffic flows at Dover Eastern Docks will remain the same as now after Brexit, it would be extremely foolish not to prepare for what could be a major problem for our town.
"We have experience of severe traffic congestion in Dover when one or more of any of a number of issues arises and the port and ferry companies cannot process the traffic in the volume it is arriving."
One of the most notorious cases was Black Saturday when vehicles, cars and lorries, tailed back deep into the town as far as the Five Ways junction at Maison Dieu Road.
On July 23, 2016, up to 250,000 motorists were delayed for up to 12 hours because of lack of French border control staff.
But Cllr Collor, who is also Dover District Council portfolio holder for access, recalled a more recent snarl-up, on July 27 and 28 this year, which brought the town centre and approach roads to a standstill.
Dover TAP was put in place but some trucks found their way around the system and there was also an excess of traffic causing problems in southern parts of the town.
He complained at the time that emergency vehicles couldn't get through, some bus services were suspended and a number of elderly residents were left waiting for their carers to visit them.
There was also a vicious circle of port staff having to walk the last part of their journeys to work, with delays in their arrival to their posts adding to delays.
Cllr Collor explained that a similar situation occurred on March 29 this year, exactly a year before Britain leaves to EU.
Tourist traffic and and the impacts on Dover are a key priority, said Cllr Whiting.
Tactics used to cope with Black Saturday will have to be brought up to date handle any post-Brexit problems.
Cllr Whiting told Cllr Collor that a number of Operation Fennel multi-agency groups are now meeting, including a task and finish group meeting every week.
That group consists of members of the Department of Transport, Kent Police, Highways England and Kent County Council's highways department.
He said: " One of the key priorities currently being discussed is the issue of tourist traffic and the impacts on Dover."
He said that after Black Saturday, agencies developed a process called Operation Perch to ensure management of tourist traffic into Dover during incidents.
He added: "The Fennel Task and Finish group is currently looking at updating the Perch document to take into account possible scenarios post-Brexit.
"The plan will need to be updated due to the possible mix of freight and tourist traffic heading to the Port.
"Once the plan has been amended it will be shared with relevant parties, including Dover District Council."
Operation Fennel is the multi-agency response to the swamping of roads from traffic unable to leave Britain via Dover and the Channel Tunnel.
It collates Kent Police, Highways England and KCC plans together as a single source Kent Resilience Plan.
Dover could be at risk of gridlock until 2023, both damaging air quality and harming businesses.
This was a warning in a report by Dover District Council in July on the implications of Brexit.
Changes to customs arrangements and border controls puts the town at risk of lengthy traffic queues.
The authority is particularly worried because of the number of lorries passing through the port on peak days and a predicted rise of 43% by 2030.
And Kent County Council has plans for a permanent lorry park that will not be ready until 2023 at the earliest.
Highways England’s Dover TAP (Traffic Assessment Project) is used with traffic lights to control the flow of lorries entering the town from the west.
It is usually from the the Round Hill Tunnels at Folkestone to Aycliffe and involves a 40 mile per hour speed limit for all traffic, where the speed limit is usually 70mph.
Operation Stack, a system used for decades, is where lorries are left to park on sections of the M20 when there are severe delays for port traffic.
This is usually because of bad weather or strikes by French workers.
The government's Operation Brock is an alternative to Stack, allowing traffic to go both ways on M20 when lorries have to be parked up.
This is through a contraflow system between Junctions 8 and 9.