More than 8,000 lorries have crossed to France since Christmas Eve, with 1,600 still waiting to cross the Channel, the Department for Transport says.
Only five vehicles, all with mechanical problems, remain at the Manston Airport site.
Lorry drivers must test negative for coronavirus before being allowed to make the crossing to France.
Transport Secretary Grant Shapps said 15,526 coronavirus tests had been carried out, with 36 positive results.
He said lorries bound for Dover and the Eurotunnel terminal at Folkestone should no longer head to Manston.
Update on Kent lorry situation: 15,526 #Coronavirus tests now carried out. Just 36 positive results, which are being verified (0.23%).— Rt Hon Grant Shapps MP (@grantshapps) December 26, 2020
Manston now empty and lorries should no longer head there please. pic.twitter.com/RPBC5Rsd2C
A spokesman for the Department for Transport (DfT) said 1,600 vehicles remained in Operation Brock and none in Operation Stack.
He said the broken down vehicles at Manston would be moved "shortly".
"Over 8,000 HGVs have passed over the border via Eurotunnel or the Port of Dover, since 23 December," he said.
Eurotunnel said it had carried 4,000 trucks to France since the border was opened, including 1,200 on Christmas Day.
'Not over yet'
John Keefe, from Eurotunnel, said: "We had more than 100 staff volunteer to come in on Christmas Day and Boxing Day to help increase the uplift by putting on extra departures.
"On Christmas Day we carried four times the original forecast level of traffic."
Duncan Buchanan, from the Road Haulage Association, said traffic was flowing in Dover, but "it's not over yet" because more drivers who held off leaving over Christmas would be joining the queue in the coming days.
"We still have all the people who delayed travelling, who will start to want to get through. Some people will have parked up in Essex and will be looking at moving again.
"Next week is a normal working week so I would expect the vehicles to increase then too. It's not over yet and we will see what happens next."
What are operations Stack and Brock?
Stack is an emergency measure designed to prevent gridlock in Kent.
Freight is separated into two queues on either side of the coast-bound carriageway between junctions 8 and 9.
One lane is used for traffic heading to the Eurotunnel terminal and one lane is for port traffic. The middle lanes are kept clear for emergency vehicles.
Non-freight traffic is diverted off the motorway and on to the A20.
Under Operation Brock, a motorway barrier system creates a contraflow on the M20 London-bound, between junctions nine and eight.
It means more of the road network can stay open and can remain in place indefinitely.
France closed its border after the UK warned of a fast-spreading variant of coronavirus but ended its ban on Wednesday, providing people tested negative before travelling.
Drivers are allowed to cross to France on the condition they test negative for Covid-19 before boarding a train or ferry.
Thousands of lorry drivers waiting to cross the English Channel to France spent Christmas Day in their cabs in Kent.
Hundreds of military personnel were deployed to help clear the backlog.