More than 10,000 coronavirus tests have been carried out in a bid to clear the backlog of lorries waiting to cross the English Channel into France.
Some 1,100 military personnel have been deployed in Kent as part of the repatriation operation, after French Covid-19 restrictions caused severe disruptions at the Port of Dover.
The British Ministry of Defence (MoD) said about 4,500 trucks had crossed the channel as of this afternoon, but added that more vehicles continue to arrive "every hour".
France's demand that drivers show proof of a negative Covid-19 test before entering the country forced thousands of international hauliers to spend Christmas Day in their cabs.
The French closed their border last Sunday following the discovery of a fast-spreading mutant Covid-19 strain in the UK, before easing restrictions on Wednesday.
About 5,000 hauliers remain unable to get home, despite some progress in testing drivers in their vehicles at nearby Manston Airport, on a closed section of the M20, and in the town of Dover itself.
Some have already spent nearly a week stranded due to the diplomatic impasse.
Army personnel have been testing drivers for coronavirus and distributing food and water, the MoD said.
A chorus of beeping horns sounded at Dover on Christmas Eve as those at the front of the queue celebrated finally being able to leave.
Traffic was moving smoothly through Dover, with French firefighters drafted in to help test drivers.
Southeastern railway and Network Rail arranged for food to be delivered to drivers stuck in Operation Brock on the M20.
Seven trains carrying crates of food for the hauliers left London, with the Salvation Army distributing the items.
The MoD said additional soldiers had been deployed today as part of Operation Rose to support the 300 personnel already there.
"We are deploying a further 800 personnel to Kent today to support an increase in the testing capabilities to help clear the backlog of vehicles and ensure traffic can begin to move at a closer to normal pace through Dover," the MoD tweeted.
Britain's transport minister Grant Shapps said in a tweet that over 10,000 Covid-19 tests have been carried out with 24 of those positive.
Update on Kent lorry situation: Over 10,000 #Coronavirus tests now carried out. Just 24 positive (0.24%).
— Rt Hon Grant Shapps MP (@grantshapps) December 25, 2020
A huge thank you for the tireless efforts of our troops, police, civilian testers, council planners & port & ferry workers for giving up their Xmas to get people home.
Earlier, he said: "We need to get the situation in Kent, caused by the French government's sudden imposition of Covid restrictions, resolved as soon as possible.
"I have today sent special instructions to the army to take control of testing and HGV management operations in the county. Our aim is to get foreign hauliers home with their families as quickly as we can.
"I know it's been hard for many drivers cooped up in their cabs at this precious time of year, but I assure them that we are doing our utmost to get them home."
The government said catering vans would provide hot food and drinks to hauliers stranded at Manston, with Kent County Council and volunteer groups providing refreshments to those stuck on the M20.
There are more than 250 toilets at Manston, with a further 32 portable toilets added to existing facilities on the M20.
A Port of Dover spokesman said ferry services ran throughout Christmas Eve night and will continue today to help ease congestion.
