Fewer than 60 lorry drivers are waiting to cross to France after thousands had queued over Christmas, the Department for Transport says.
Hauliers had to wait to cross the Channel after France closed the border on 20 December following a UK alert over a new Covid-19 variant.
By Monday, 59 HGVs were waiting in Kent, the DFT said.
Since the border reopened, following an agreement reached on 22 December, 14,659 lorries have crossed to France.
Traffic flow systems used during cross-Channel disruption came into force over the last week, including Operations Brock and Stack, where lorries queue on the M20 and use lorry parks, including the site at Manston Airport.
At one stage, about 5,000 lorries were waiting at Manston and hundreds of military personnel were deployed to help clear the backlog.
Transport Minister Robert Courts said: "With progress made on clearing the Manston site and work on getting hauliers holding in Operations Brock and Stack moving, there is light at the end of the tunnel."
Drivers must now show proof of a Covid-19 negative test before they can enter France from the UK.
Transport Secretary Grant Shapps said on Monday that 21,849 coronavirus tests had been carried out, with 66 positive results. He also said the M20 had been reopened.
Many of the lorries that crossed were carrying a driver and also one passenger or more.
Update on #Kent lorry situation: 21,849 #Coronavirus tests now carried out. Just 66 positive results (0.30%).— Rt Hon Grant Shapps MP (@grantshapps) December 28, 2020
M20 open again but follow @KentHighways & @HighwaysEngland for latest updates before travelling to Kent. Current delay for Eurotunnel & Ferry is 30mins for test result.
Volunteers and organisations including HM Coastguard, Kent County Council and the Road Haulage Association (RHA) delivered meals and water to drivers, and Tesco and Eddie Stobart Logistics provided food parcels.
RHA chief executive Richard Burnett said: "Nothing can compare to spending Christmas with the family. These drivers have been denied that through no fault of their own."