More than 30 countries have banned UK arrivals because of concerns at the spread of a new variant of coronavirus.
Flights from the UK have been suspended in nations in Europe and across the world including India and Hong Kong.
On Sunday evening, France shut its border with the UK for 48 hours, meaning no lorries or ferries will be able to sail from the port of Dover.
The French government said on Monday it will establish a protocol “to ensure movement from the UK can resume”.
The prime minister is due to chair a meeting of the government’s emergency committee and will hold a press conference at Downing Street later.
European Union member states are currently meeting in Brussels to discuss a co-ordinated response.
In a post shared on Twitter by the French Embassy in the UK, French Transport Minister Jean-Baptiste Djebbari said: “In the next few hours, at European level, we’re going to establish a solid health protocol to ensure that movement from the UK can resume.”
He added the “priority” was to “protect our nationals and our fellow citizens”.
Eurotunnel spokesman John Keefe said he hoped travel from the UK to France could begin on Wednesday or Thursday.
“We expect it will be something around testing,” he told BBC Radio 5 Live.
Other countries to impose a ban on UK arrivals include Belgium, Canada, Germany, Ireland, Italy, Romania, Russia and Switzerland.
Meanwhile, coronavirus cases in the UK rose by 35,928 on Sunday – nearly double the number recorded seven days previously.
And it was announced that a further 326 people died within 28 days of testing positive, bringing the nation’s total to 67,401.
Health Secretary Matt Hancock warned that the new variant of the virus – which may be up to 70% more transmissible – is “getting out of control”.
The new variant has spread quickly in London and south-east England, but health officials say there is no evidence that it is more deadly or would react differently to vaccines.
On Monday, Labour leader Sir Keir Starmer called on Prime Minister Boris Johnson to address the nation on coronavirus following his emergency meeting.
Sir Keir said: “The news over the last 24 hours has been deeply disturbing. The number of coronavirus cases has nearly doubled in the last week.”
Citing international borders closing and “severe disruption” at Britain’s ports, he said: “Make no mistake this is now a real emergency.”
He called on the government to step up, saying: “We can have no more over-promising and false hope, confused messages and slow decision-making. We need strong, clear and decisive leadership.”