The M20 has been closed London bound to increase capacity for lorries to wait before crossing the Channel.
Residents in Kent have been told to avoid using the road or the A20 this evening as it is shut between Junctions 9 (Ashford) and 8 (Leeds Castle).
Tensions have been rising on the approaches to the Port of Dover after stranded drivers were told they would have to leave the town to rejoin huge queues of lorries at Manston Airport and in the Operation Brock system on the M20.
Despite coronavirus testing being carried out for drivers and Eurotunnel now starting to move lorries from the roads in Kent, queues on the M20 have continued to grow - with Operations Stack and Brock reaching capacity.
The M20 coastbound was already shut and is being used to stack lorries until disruption eases.
Additional measures have now been taken to manage the situation.
Maidstone Borough Council chief executive Alison Broom said: "We realise that this has been a very difficult time for our residents and the issues on the M20 have impacted our communities, but we are asking them to not make journeys unless it is absolutely necessary tonight.
"The A20 and M20 are two very busy and vital routes through the borough of Maidstone so it is imperative that we get the motorway clear as quickly as possible whilst at the same time supporting the lorry drivers who have been waiting there to be able to travel through the Port of Dover or Eurotunnel.
"Please think about if you really need to make that journey tonight as if you don’t you will be avoiding what could be potentially long delays and helping to keep our roads clear for essential traffic including the emergency services.”
Diversion routes will be put in place.
All agencies are working to enable freight and passenger journeys to be completed as soon as is practicable and for these temporary traffic management arrangements to be reversed so that only Operation Brock remains in preparation for EU Transition.
Drivers are facing "bedlam" on the A20 as the situation on Kent's roads worsens.
Traffic is at a near standstill around Hythe, with delays stretching all the way back to Mersham near Ashford.
It comes after lorry drivers clashed with police and blockaded the Port of Dover as tensions rise over testing soar.
The giant makeshift 4,000-capacity lorry park at Manston Airport is full.
Drivers stranded in the county since the border was shut on Sunday need to get tested before being allowed to cross the Channel.
Many have been stranded at the port due to fears over the "out of control" new coronavirus strain.
The ban was lifted last night but drivers must test negative at Manston Airport before they make the trip.
Thousands of lorries remain stranded in Kent and it could take days to clear the backlog - with one haulage boss declaring the situation an "humanitarian crisis".