LONDON — The British authorities put even more areas of England under the tightest restrictions on Wednesday as officials struggled to slow the spread of a coronavirus variant that is potentially more infectious than those that have already wreaked havoc around the world.

The French government lifted a 48-hour blockade of the British border that was aimed at preventing the new variant from spreading. But the effort on Wednesday to get traffic moving descended into chaos as officials struggled to carry out the tests required for thousands of drivers stuck at English ports to leave the country.

By Wednesday night, traffic began to move again, according to the British Broadcasting Corporation. But more than 5,000 Europe-bound trucks are still jammed up near the port of Dover, across the English Channel from France. Frustrated drivers fumed over the prospect of a fourth night sleeping in their vehicles. One transport company said its drivers had to throw away more than 100,000 pounds of spoiled food.

With uncertainty swirling around the looming Dec. 31 deadline for a post-Brexit trade deal, a virus spreading at astonishing speed, exhausted health care workers struggling with an influx of patients, and millions of people confined to their homes as holiday lights glimmered on deserted streets, the Christmas season was shaping up to be uniquely brutal.

Adding to that pain, Britain relies on importing fresh fruit and vegetables, especially in the winter. Supermarkets have tried to reassure customers that there is enough food, but they cautioned that some fresh goods could run short later in the week if delays continued.

Tesco, one of Britain’s largest grocery chains, emailed customers on Tuesday to say it had “good availability” of items imported from France but that it had imposed temporary purchasing limits on some items, including eggs and toilet paper.

The most pressing concern, British officials said, was slowing the rapid spread of the virus, which they attributed to the efficiency of the new variant. Britain reported 39,237 cases on Wednesday, up 56 percent from a week ago, according to a The New York Times database.

The number of people in the hospital — nearly 19,000 — is close to where it was at the peak of the outbreak in the spring. And 744 deaths were reported on Wednesday.

“Against this backdrop of rising infections, rising hospitalizations and rising numbers of people dying of coronavirus, it is vital that we act,” said Matt Hancock, the British health secretary.

Areas in southern and eastern England — including Cambridgeshire, Norfolk, Oxfordshire, Suffolk and Sussex, — are set to move to the highest level of restrictions starting Saturday, joining London and much of southeastern England. The rules require people to stay at home except for urgent travel, medical appointments and outdoor exercise, and Mr. Hancock said limiting human contact was the only way to protect people.

British officials also expressed concern about the spread of another virus variant identified in South Africa. Mr. Hancock said it was even more easily transmitted than the mutation that prompted the lockdowns in England.

Scientists are currently studying both of the newly discovered variants. While early indications suggest they are both more transmissible, more laboratory tests are needed to gain a fuller understanding of the dangers they pose.

Mr. Hancock said that the British authorities had detected two cases of the South African variant. In both cases, the infected people had been in contact with people who had traveled to Britain from South Africa in recent weeks.

Those infected with the new variant and their close contacts would be quarantined, and Mr. Hancock said that travel from South Africa would be restricted. At least five other countries have put in place similar restrictions on travelers from South Africa.

More than 50 governments have barred travelers from Britain since Saturday, when Prime Minister Boris Johnson first raised the alarm over the variant spreading in England and imposed the new lockdown.

French officials also blocked freight shipments for 48 hours, saying the border closure was needed to establish testing protocols given the alarm over the variant.

The British Army was mobilized to help the National Health Service, the country’s health care system, to set up facilities to administer rapid coronavirus tests to drivers and went truck to truck to conduct tests.

But it was slow going.

On Wednesday, with traffic largely at a standstill, drivers who had already spent days in their rigs were left frustrated and confused about how to get a test.

As tensions boiled over, police officers clashed with angry drivers, desperate to get home for Christmas. TV footage showed scenes of pushing and shoving. The police in Kent, which includes the port of Dover, said at least one arrest had been made.

There was concern that the mess on Wednesday could be a prelude to the logistical nightmare to come, particularly if trade talks between Britain and the European Union end without a deal.

Tom Binks, the managing director of Peter Green Chilled, a refrigerated and frozen food transport company, said his drivers have had to throw away more than 100,000 pounds of lamb, poultry, cheese and yogurt since Monday. But even before the border was closed this week, he said, his drivers had already waited as long as six hours at the port of Dover this month.

“The port is basically overwhelmed,” Mr. Binks said, adding that it lacked the infrastructure to handle the increased shipment volumes as the pandemic and Brexit set off panic buying. “And then the decision from the French on top of it. It’s just unbelievable.”

He said that delivery volumes have been 70 percent higher this month than other months because of increased orders for Christmas and Covid-19 and Brexit stockpiling. In past years, delivery volumes in December have been up 30 percent compared to the rest of the year, he said.

The authorities cautioned that it could take days to clear out the more than 5,000 trucks bound for Europe.

“I think it will take a few days to work our way through,” Robert Jenrick, a government minister, said on Sky News on Wednesday. He also said any drivers who tested positive would be offered a more accurate P.C.R. test, which takes longer to process. If that were also positive, they would be offered hotel accommodation to isolate for 10 days.

Rod McKenzie, the director of policy at Road Haulage Association, which represents the British road transport industry, said probably 8,000 to 10,000 trucks were waiting to cross the border.

“It’s a mammoth task,” he told Sky News.

Some drivers have already spent three nights sleeping in their trucks with limited access to food and toilets and were looking at a fourth on Wednesday. Trucks carrying goods to Britain from continental Europe were allowed to pass through ports this week, but their numbers declined amid fears that the drivers would be stuck once they crossed into Britain.

Mr. Binks, the managing director of the transport company, said he was most worried about what happens after Dec. 31, when Britain is no longer part of the European Union’s single market and customs union.

“We’ve got maybe 15 trucks heading out next week, and I don’t know whether to send them or not,” he said. Food shortages and further disruptions to deliveries are inevitable, he said.

Constant Méheut contributed reporting from Paris.