More than 40 countries have banned UK arrivals because of concerns about the spread of a new variant of coronavirus.
Flights from the UK are being suspended to countries across the world including Spain, India and Hong Kong.
France shut its border with the UK for 48 hours, meaning no lorries or ferries can leave from the port of Dover.
Boris Johnson is chairing a meeting of the government’s emergency committee and will hold a press conference at Downing Street at 17:10 GMT.
He will be joined by Transport Secretary Grant Shapps and Sir Patrick Vallance, the UK government’s chief scientific adviser.
It comes as the French government said it will establish a protocol “to ensure movement from the UK can resume”.
European Union member states are currently meeting in Brussels to discuss a co-ordinated response, with officials suggesting a requirement for tests could be imposed on all people arriving from the UK.
Other countries to impose a ban on UK arrivals include Belgium, Canada, Germany, Ireland, Italy, Portugal, Romania, Russia, and Switzerland.
Some of the bans are already in force while others are to begin on Tuesday.
Eurotunnel services to France are also suspended and Eurostar trains to Belgium are not operating.
However, Eurotunnel spokesman John Keefe said he hoped travel from the UK could begin on Wednesday or Thursday.
The latest figures released on Monday reveal that another 33,364 people in the UK have tested positive for coronavirus.
There were also a further 215 deaths within 28 days of testing positive, bringing the nation’s total to 67,616.
Health Secretary Matt Hancock has 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.
Labour leader Sir Keir Starmer described the situation as a “real emergency”, saying: “The news over the last 24 hours has been deeply disturbing. The number of coronavirus cases has nearly doubled in the last week.
“We can have no more over-promising and false hope, confused messages and slow decision-making. We need strong, clear and decisive leadership.”
Scotland’s First Minister Nicola Sturgeon said the government had plans for coping with port disruption in the event of a no-deal Brexit and should now activate the measures.