Retailers have played down fears of immediate food shortages after France shut its borders to UK hauliers for 48 hours.
However, they warned of “serious disruption” if the blockade is prolonged.
France made the move over fears about the UK’s new coronavirus variant.
Sainsbury’s warned it could face “gaps” in some of its fresh food supplies within days if the UK and France failed to resolve the issue.
The Channel is a vital trade route, with about 10,000 lorries a day travelling between Dover and Calais in peak periods such as Christmas, largely bringing in the freshest produce.
The risk is European hauliers will avoid the UK for fear of getting stranded in the country.
The head of the Food and Drink Federation (FDF), Ian Wright, said the border closure had the “potential to cause serious disruption to UK Christmas fresh food supplies – and exports of UK food and drink”.
Andrew Opie, director of food & sustainability at the British Retail Consortium, said retailers had stocked up well ahead of Christmas.
But he added: “The closure of France to UK traffic, including accompanied freight poses difficulties for UK capacity to import and export key goods during the busy Christmas period.
“While goods can enter from France, few haulage firms will be willing to send trucks and drivers across to the UK without a guarantee they can return to the EU in a timely manner.”
A Sainsbury’s spokesman said all of its Christmas lunch products were “already in the country and we have plenty of these”.
“We are also sourcing everything we can from the UK and looking into alternative transport for product sourced from Europe,” he said.
But he added: “If nothing changes, we will start to see gaps over the coming days on lettuce, some salad leaves, cauliflowers, broccoli and citrus fruit – all of which are imported from the Continent at this time of year.
“We hope the UK and French governments can come to a mutually agreeable solution that prioritises the immediate passage of produce and any other food at the ports.”
Currently freight lorries cannot cross by sea or through the Eurotunnel to France, but trucks coming in the opposite direction are still allowed.
Unaccompanied freight, such as containers or lorry trailers on their own, can still be transported from the UK to France.
UK ministers will discuss the French ban at a Cobra emergency committee on Monday after urging the public and hauliers not to travel to ports in Kent such as Dover.
Transport Secretary Grant Shapps said most cross Channel trade would be unaffected by the ban and that he and his French counterpart were working to resolve the blockade, for example through a mass testing programme.
However, he said that any disruption would “hang on how long these things go on”.
“The shops are well stocked. So in the short term, for the next 48 hours or so, this is not an issue in terms of supply but we’re very very keen to get it resolved,” he told the BBC’s Today programme.
“It is actually French and European hauliers who are getting caught up in this and they sell more to us than we sell back to them,” he added.
Kent Police have also mobilised Operation Stack – a system to park lorries on the M20 motorway in Kent- to handle the build-up of traffic caused by the disruption.
The force said it had implemented the closure of the coast-bound carriageway of the motorway between Junctions 8 and 11 as a “contingency measure”.
The Department for Transport has said that Manston Airport in Kent is being readied to take up to 4,000 lorries to ease congestion in the county.
The Port of Dover is closed to traffic leaving the UK “until further notice” due to border restrictions in France, port authorities said on Sunday.
“Both accompanied freight and passenger customers are asked not to travel to the port,” it said.
Richard Burnett, head of the Road Haulage Association, told the BBC’s Today programme that consumers should not “worry about panic buying at this point in time”.
He also said retailers would be doing all they could to ensure their fresh food supplies.
“The retailers will absolutely be assessing their inbound flows this morning and understanding whether or not those flows are on their way into the retail distribution centres around the country and I’m sure there will be further reassurance given today that those things are in control.”
Another freight industry lobby group, Logistics UK, said it was concerned about the welfare of drivers going from the UK to France, and said they should have access to regular testing.
It appealed for calm from shoppers, and said it was “maintaining close contact with UK government to ensure that supplies of fresh produce are available throughout Christmas and the new year”.
The government does not think the restrictions will affect the delivery of Covid-19 vaccines to the UK, Transport Secretary Grant Shapps told the BBC.
However, Labour’s Rachel Reeves, shadow minister for the Cabinet Office, called the developments “deeply worrying”.
“The country needs to hear credible plans and reassurance that essential supplies will be safeguarded, including our NHS, supermarkets and manufacturers with crucial supply chains,” she said.
Scotland’s First Minister Nicola Sturgeon has called on the government to extend the Brexit transition period as it deals with the new coronavirus variant, saying it was a “profoundly serious situation” which “demands our 100% attention”.
The current transition period is due to expire at the end of the year and the EU and UK are still negotiating a trade deal.
Without it both sides will have to collect expensive tariffs that the Office for Budget Responsibility says could harm the UK’s economy.
The block on freight traffic into France came as a number of European countries banned flights and other travel from the UK over fears about VUI – a mutation of the coronavirus that is spreading rapidly in the UK.
France, Italy, Ireland, Germany, Belgium the Netherlands and Turkey are among those to have banned flights from the UK while other nations are considering the move.