Video report by ITV News Political Correspondent Libby Weiner
The EU has said nations should end their travel bans on the UK in order to avoid further disruption as more than 2,800 lorries remain held up in Kent.
Many nations banned flights to the UK and France closed its borders in a bid to prevent the spread of a highly transmissible new Covid variant.
The European Commission recommended on Tuesday that flight and train bans on travel from the UK should be discontinued to avoid supply chain disruptions, but “non-essential travel to and from the UK should be discouraged”.
Transport Secretary Grant Shapps tweeted: "Good progress today and agreement with the French Government on borders."
He also said there would be an update on hauliers tonight before warning "hauliers must still not travel to Kent this evening."
EU justice commissioner Didier Reynders said: "Member states should take co-ordinated action to discourage non-essential travel between the UK and the EU.
"At the same time, blanket travel bans should not prevent thousands of EU and UK citizens from returning to their homes."
Transport commissioner Adina Valean said: "Within the EU, it is crucial that transport workers are exempted from any restrictive measures."
The closure of French ports and the Euro tunnel has led to chaos in Kent as lorries were forced to queue up for miles along the M20.
Trucks have also been queuing on the main road outside Manston Airport, near Ramsgate, which is being used as a lorry park.
A steady stream of lorries continue to enter the site, which is next to a drive-through coronavirus testing facility, while trucks can be seen lined up on the runway of the disused airfield.
The Road Haulage Association has expressed concern about the access to facilities and support for drivers, who were forced to sleep in their vehicles overnight.
Drivers facing their second night sleeping in their vehicles at Manston protested on Tuesday afternoon by honking their horns.
Laszlo Baliga, who was delivering food and water to those parked at Manston, said one driver had told him the only toilet on the site was blocked.
“No water and no toilet now – there is one toilet, but it is now blocked,” the 51-year-old told said.
Mr Baliga, from London, who himself is a lorry driver, said he began taking supplies to the disused airfield after Hungarian drivers posted on Facebook asking for help.
"We have taken money from friends and gone to Asda, Tesco,” he said.
"This is our third time, we have already brought ready-to-eat sausages, bread, tomatoes, iceberg lettuce, coffee. Basic foods for now for the drivers."
He said he and others have spent more than £500 on food and water for drivers inside the site.
“We like to help because this is a difficult time," he said.
ITV News Correspondent Rebecca Barry was in Manston, Kent:
Kent County Council said by Tuesday afternoon more than 2,800 lorries were being held up by the ban on travel to France.
A spokeswoman said about 2,180 lorries were being held at the former Manston airfield while 632 were part of the Operation Stack arrangements on the M20.
There are concerns that because the initial 48-hour restrictions imposed by France are due to expire, more drivers may take a risk and head to Dover.
“The message here is not to come to Kent because the border is closed,” the spokeswoman said.
Ms Patel said: "These numbers fluctuate all the time and we know lorries are travelling around the country and then they're coming back to Dover.
"But also, right now, we have Operation Stack underway which basically is a contraflow system to move lorries away from queuing and take them to Manston where we have facilities for them and welfare sites in particular."
Ian Wright, chief executive of the Food and Drink Federation (FDF), also told MPs that he believes at least 4,000 trucks could be impacted by the blockage at the port of Dover.
“I don’t think the number of trucks in the queue or other areas is the relevant number,” he said. “We reckon about 4,000 on their way to Dover at various points."
Mr Wright added that "dozens of lorries (are) there with product that is going off" adding: "There is a huge hit here to Scottish seafood.
"The Government was well aware of the power of the announcement it made on Saturday and Chris Whitty went out of his way to rightly scare people over the impact.
“Everyone would have rightly known that everyone in Europe would have reacted this way, and in fact we felt similarly with Danish mink were infected.
“The consequence of this is the chaos we’ve seen over the past 24 hours. It’s incumbent on the Government to come forward to compensate on those who have lost out due because of that failure of authority.”
Duncan Buchanan, director of policy, England and Wales, at the Road Haulage Association, told MPs he was disappointed with how Government presented the levels of freight disruption on Monday evening.
"It was seeking to minimise the nature of the problem,” he told MPs at the business, energy and industrial strategy select committee.
Andrew Opie, director of food and sustainability at the British Retail Consortium (BRC), told the committee: "If we do not see the empty trucks, which have already delivered to warehouses and stores, getting back over the channel, they will not be able to pick up the next consignment of fresh fruit, vegetables, salad vegetables, all the food we do not grow in the country at this time of year."
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.
ITV News understands that Eurotunnel was to bring 2,000 lorries into the UK on Tuesday but will not take any out of the UK.
Managing director of the Road Haulage Association, Rod McKenzie said stranded lorry drivers waiting to cross the Channel on Monday evening were offered just a single cereal bar each by Kent County Council.
Mr McKenzie told BBC Breakfast: "Clearly those drivers have spent a second night parked up somewhere, possibly on a motorway, possibly somewhere else, trying to get across the Channel, and many of them are European drivers trying to get home for Christmas, and their morale is very poor.
"Yesterday Kent County Council offered each of them one cereal bar, which is a pretty poor effort, I think in terms of maintaining their morale, and their spirits."
Shadow chancellor of the Duchy of Lancaster Rachel Reeves said lorry drivers are essential workers and should be treated “a lot better".
Nicola Sturgeon has urged the UK government to reach an agreement with France "without delay" adding that the border closure is having a serious impact on exporters including Scottish seafood traders.