Talks with France on resuming full trade and transport across the Channel were continuing on Tuesday amid warnings that the border must be running again by Wednesday to avoid disruption to food supplies.
Home Secretary Priti Patel said the Government is "speaking constantly" with France to achieve a resolution "in both our interests" to get freight moving again.
More than 40 countries have banned flights from the UK due to a mutant variant of coronavirus spreading through the country, while lorry drivers spent a second night sleeping in their cabs on the M20 outside the Port of Dover, which has been shut since Sunday night.
Reports suggest a possible solution could be mass testing of HGV drivers across the Channel, while the BBC reported that plans to reopen the border will come into effect from Wednesday, citing French Europe Minister Clement Beaune.
Andrew Opie, director of food and sustainability at the British Retail Consortium, said the "borders really need to be running pretty much freely from tomorrow to assure us that there won't be any disruption".
He told BBC Radio 4's Today programme: "There is a problem potentially directly after Christmas and that is really in fresh produce, so we're talking here about things like salad, vegetables, fresh fruit, of which the vast majority come from Europe at this time.
"The problem actually is empty lorries, so the empty lorries which are now stuck in Kent, they need to get back to places like Spain to pick up the next consignment of raspberries and strawberries and they need to get back within the next day or so, otherwise we will see disruption."
He added: "As long as it can be cleared today, there'll be minimal impact for consumers – remember the shops are shut on Christmas Day which takes one day of buying out of the equation, but those lorries that are stuck in Kent, they do need to get back within the next day."
Ms Patel told Sky News: "We speak to our colleagues in France constantly on a range of issues and that work has been under way over the last 24 hours and will continue today.
"We're working to get a resolution, I think that's really important to put this into context. It's in both our interests, both countries to ensure that we have flow, and of course there are European hauliers right now who want to be going home and, quite frankly, it's in both our interests to carry on those discussions and negotiations and we will see what materialises today."
Government sources told the PA news agency that discussions with the French government are "ongoing" after Prime Minister Boris Johnson said on Monday evening that the two countries are working "to unblock the flow of trade as fast as possible".
Pictures of the week: December 20 - 26
Pictures of the week: December 20 - 26
A Polish lorry driver, who has fashioned a makeshift Christmas tree out of empty Heineken cans, waits at a truck stop near Folkestone, Kent. Hundreds of travellers are spending Christmas Day as they wait to resume their journey to the Port of Dover and across The Channel now that the borders with France have reopened. (Photo by Gareth Fuller/PA Images via Getty Images)
Jack, 7, stands in flood water in Great Barford in Bedfordshire, after residents living near the River Great Ouse in north Bedfordshire were "strongly urged" to seek alternative accommodation due to fears of flooding. (Photo by Joe Giddens/PA Images via Getty Images)
Swimmers in Santa hats line up ready to take a Christmas Day dip at the Serpentine, in central London. The Peter Pan Cup, the race organised annually on Christmas Day by the Serpentine Swimming Club, has been cancelled due to the coronavirus restrictions in Tier 4 London. (Photo by Aaron Chown/PA Images via Getty Images)
A woman wearing a face mask passes a billboard on Oxford Street, London. Prime Minister Boris Johnson cancelled Christmas for almost 18 million people across London and eastern and south-east England following warnings from scientists of the rapid spread of the new variant of coronavirus.
Children's playground equipment pokes out from floodwater surrounding Tewkesbury Abbey, where flood watches are in place with more wet weather expected in the coming days.
LONDON, ENGLAND - DECEMBER 23: D-Day veteran and Chelsea Pensioner Bob (Robert) James Sullivan, 98, a resident at the Royal Hospital Chelsea, is applauded by staff after receiving an injection of the Pfizer/BioNTech Covid-19 vaccine from Pippa Nightingale, Chief Nurse at the nearby Chelsea and Westminster Hospital on December 23, 2020. Chelsea Pensioners are all former soldiers of the British Army over the age of 65, who reside at the Royal Hospital Chelsea, founded by King Charles II in 1682, and wear a uniform which includes a scarlet coat. (Photo by Aaron Chown - WPA Pool/Getty Images)
A french firefighter from the Sapeurs-Pompiers du Nord, who has been deployed from France to assist in testing, conducts a COVID-19 test on a driver at the Port of Dover, Kent, where thousands are waiting to resume their journey across The Channel after the borders with France reopened. Delays continue as travellers must be able to show proof of a negative test result carried out within the past 72 hours in order to be able to cross into France. (Photo by Aaron Chown/PA Images via Getty Images)
A jogger passes The Palace of Westminster as he runs along south bank of the River Thames in London on December 24, 2020, as Britain and the EU wait for a final announcement to be made on a successful post-Brexit deal. - The pound and European stock markets rose Thursday with Britain and the EU finally expected to announce a post-Brexit trade deal. (Photo by DANIEL SORABJI / AFP) (Photo by DANIEL SORABJI/AFP via Getty Images)
Larry the cat, Chief Mouser to the Cabinet Office catches a pigeon as journalists await results of the Brexit trade deal in Downing Street in London, Thursday, Dec. 24, 2020. European Union and British negotiators are closing in on a trade deal with only a disagreement over fishing remaining, After resolving a few remaining fair competition issues, negotiators were dealing with EU fisheries rights in U.K. waters Wednesday as they worked to secure a deal for a post-Brexit relationship after nine months of talks. (AP Photo/Frank Augstein)
A cleaner sweeps the pavement front of 10 Downing Street in London, Thursday, Dec. 24, 2020. Negotiators from the European Union and Britain worked through the night and right into Christmas Eve to put the finishing touches on a trade deal that should avert a chaotic economic break between the two sides on New Year’s Day. (AP Photo/Frank Augstein)
Cars drive towards check-in at the Port of Dover in Kent, after French authorities announced that journeys from the UK will be allowed to resume after the coronavirus ban was lifted, but those seeking to travel must have a negative test result.
LONDON, Dec. 22, 2020 -- The facade of the Fortnum and Mason food store is seen decorated in the style of an Advent calendar in London, Britain, Dec. 22, 2020. (Photo by Han Yan/Xinhua via Getty) (Xinhua/Han Yan via Getty Images)
Police hold back drivers trying to enter the Port of Dover in Kent after French authorities announced that the coronavirus ban was lifted and journeys from the UK will be allowed to resume, but that those seeking to travel must have a negative test result.
Nurse Heather Ong (right) gives Frewyne Hadera the Pfizer-BioNTech vaccine at the Thackray Museum of Medicine in Leeds, the first UK museum to host a COVID-19 vaccination centre, as BioNTech boss Ugur Sahin says he is confident vaccine will work on UK variant.
LONDON, ENGLAND - DECEMBER 23: Eden Silva plays a backhand shot during their round robin match against Katy Dunne during Day Four of the Battle of the Brits Premier League of Tennis at the National Tennis Centre on December 23, 2020 in London, England. (Photo by Tom Dulat/Getty Images for LTA)
Drivers block an arriving lorry from exiting the the Port of Dover in Kent after French authorities announced that the coronavirus ban was lifted and journeys from the UK will be allowed to resume, but that those seeking to travel must have a negative test result.
A drive sits in the cab of his lorry while parked on the M20 in Kent after the Port of Dover was closed after the French government's announcement it will not accept any passengers arriving from the UK. France appears set to end a ban on hauliers crossing the Channel which was imposed due to fears about the spread of the new coronavirus strain.
LONDON, ENGLAND - DECEMBER 21: Christmas decorations line a street near Tower Bridge on December 21, 2020 in London, England. Many Christmas events have been cancelled this year due to the Coronavirus Pandemic but London is festooned with Christmas Lights across the capital. (Photo by Joseph Okpako/Getty Images)
A man dressed as Santa Claus waves to patient Emma from a cherry picker outside Leeds Children's Hospital in Leeds, England, Monday Dec. 21, 2020. "Operation Airborne Santa" transported Santa using the cherry picker to all four floors of the hospital to talk to patients from a safe distance, after visits to the wards were stopped to prevent the spread of the coronavirus among patients, their families and hospital staff. (Danny Lawson/PA via AP)
Gabriel Clemens (left) and Nico Kurz (right) during day seven of the William Hill World Darts Championship at Alexandra Palace, London. (Photo by Adam Davy/PA Images via Getty Images)
Empty check-in lanes at the Port of Dover in Kent which has been closed after the French government's announcement it will not accept any passengers arriving from the UK for the next 48 hours amid fears over the new mutant coronavirus strain.
LONDON, ENGLAND - DECEMBER 21: A Christmas light installation stands near London City Hall on December 21, 2020 in London, England. Many Christmas events have been cancelled this year due to the Coronavirus Pandemic but London is festooned with Christmas Lights across the capital. (Photo by Joseph Okpako/Getty Images)
Burnley's Ashley Barnes, centre, celebrates with teammates after scoring his side's opening goal during the English Premier League soccer match between Burnley and Wolverhampton Wanderers at the Turf Moor stadium in Burnley, England, Monday, Dec. 21, 2020. (Gareth Copley/Pool via AP)
LONDON, ENGLAND - DECEMBER 20: The Salisbury pub in Covent Garden offers take away beer as new lockdown restrictions come into effect on December 20, 2020 in London, England. London and the South East enter a 'Tier 4' lockdown as a new coronavirus strain is detected in the lead up to Christmas. (Photo by Joseph Okpako/Getty Images)
Police and port staff turn away vehicles from the Port of Dover in Kent which has been closed after the French government's announcement it will not accept any passengers arriving from the UK for the next 48 hours amid fears over the new mutant coronavirus strain.
DECEMBER 20th 2020: Emergency lockdown restrictions are imposed in The United Kingdom during the worldwide coronavirus pandemic as health officials take measures to prevent a new variant of the virus from affecting greater Europe. - File Photo by: zz/KGC-246/STAR MAX/IPx 2020 3/19/20 Idle passenger airplanes parked on the apron at Manchester Airport on March 19, 2020 as The Coronavirus limits air travel around the world. (Manchester, England, UK)
A DFDS ferry leaves from the Port of Dover which has been closed after the French government's announcement it will not accept any passengers arriving from the UK for the next 48 hours amid fears over the new mutant coronavirus strain.
Shoppers wearing face masks walk on the street.
Prime Minister Boris Johnson announced on Saturday 19 December, that London and South East of England will move into Tier four restrictions and asked people to 'stay at home'. (Photo by Dinendra Haria / SOPA Images/Sipa USA)
A sign on the M56 motorway informs drivers that all routes into France are closed at the junction with the M6 at Lower Stretton near Warrington, northwest England, on December 21, 2020. - The British prime minister was to chair a crisis meeting on December 21 as a growing number of countries blocked flights from Britain over a new highly infectious coronavirus strain the UK said was "out of control". Crucial transit country France moved to block people and goods crossing the Channel, while the Netherlands said passengers arriving by ferry would be denied entry. (Photo by Paul ELLIS / AFP) (Photo by PAUL ELLIS/AFP via Getty Images)
LONDON, ENGLAND - DECEMBER 20: People order takeout at restaurants in Chinatown on December 20, 2020 in London, England. London and the South East enter a 'Tier 4' lockdown as a new coronavirus strain is detected in the lead up to Christmas. (Photo by Joseph Okpako/Getty Images)
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The M20 in Kent was closed on Monday night to allow for the implementation of Operation Brock – contingency measures which involve using a moveable barrier to keep traffic moving on the motorway whenever there is disruption at the Channel.
Meanwhile, the Government's chief scientific adviser, Sir Patrick Vallance, said tougher restrictions may be needed across the UK because cases of the mutant strain of Covid-19 are now appearing "everywhere" and it is transmitted more easily.
London and parts of southern and eastern England were rushed into the new Tier 4 lockdown regime at the weekend, effectively cancelling Christmas plans and imposing measures similar to the previous national lockdowns.
At a Downing Street news conference on Monday, Sir Patrick said: "I think it is likely that this will grow in numbers of the variant across the country, and I think it's likely, therefore, that measures will need to be increased in some places, in due course, not reduced."
Scotland and Northern Ireland have already announced new lockdowns from Boxing Day, while Wales's tough restrictions will only be eased for Christmas Day before being reimposed.
Northern Ireland's Executive voted against imposing a travel ban on Great Britain and the Republic of Ireland overnight but did agree to issue guidance warning against all but essential travel.
But more positive news came from the Prime Minister, who said more than 500,000 people have now received their first dose of the Pfizer/BioNTech Covid-19 vaccine.