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Operation Brock caused severe traffic problems on both the M20 and M2, with traffic queueing for miles for much of the day.
Motorists faced heavy congestion on the M20 from Junction 8 near Leeds Castle and the Maidstone Services to Junction 7 at Detling.
The coastbound carriageway has been closed with traffic cameras showing queues that earlier this afternoon stretched back five miles.
Drivers faced up to 50 minute delays.
Police were on the scene with National Highways to assist with traffic management.
Nationals Highways advised non-EU freight traffic to follow the hollow circle diversion symbol and leave the M20 at J8 and take the second exit at the roundabout onto the A20 eastbound towards Ashford.
From there they should follow the A20 through Harrietsham, Lenham and Charing to the Drovers roundabout and take the first exit to continue on the A20 towards the M20.
Drivers should then carry on along the A20 to the M20 J9 roundabout and take the 3rd exit onto the M20 coastbound.
EU traffic is being told to leave the M20 at the J8 slip road and rejoin the M20 via the entry slip road at the same junction.
Meanwhile, there are long delays and queueing traffic on the coastbound M2 from Junction 3 for Chatham, Rochester and Maidstone to Junction 7 at Brenley Corner.
There have also been bad delays in Folkestone and Dover today.
This morning's bad weather is still impacting the Port of Dover, with ferry firm DFDS reporting disruption to services.
A spokesman said: "Due to adverse weather conditions & technical issues, we are currently experiencing delays on all of our crossings.
"To our customers already checked in at our ports, please be assured we have our DFDS representatives in the car lanes who will be able to assist you."
It comes as P&O ferries are still not running from the port – two weeks after it sacked 800 workers and brought in replacement agency staff.
Dover TAP was also in place today.
This involves lorries queuing on one side of the A20 on approach to Dover, so that the town does not get congested.
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Earlier today, queues reached as far back as Folkestone.
The Roundhill Tunnel was also closed coastbound. This caused delays from J13 to J11 of the M20.
A diversion was in place along the A259 and A260 but the tunnel reopened at about 7.30pm.
There also continue to be problems on the A2 where Jubilee Way is closed coastbound due to lorries waiting to get on a ferry and to stop more from joining between the A256 Whitfield roundabout and the Eastern Docks roundabout.
This morning, Scott Janaway tweeted: "My daughter's been stuck on the A2 just before the Whitfield roundabout north bound for over an hour. Because of lorry’s blocking both lanes. What’s going on?"