Boris Johnson will chair an emergency Cobra meeting after the France-UK border closure brought Dover ferry traffic and rail services to a standstill.
Ireland and France have become the latest in a growing list of European countries to ban travel from the UK in an attempt to curb the spread of the new variant of Covid-19.
The Eurotunnel announced it was suspending access to its Folkestone terminal on Sunday after the spread of a new strain of Covid-19 prompted France, Germany, Italy, Belgium, Austria and the Netherlands to halt flights arriving from the UK.
A Downing Street spokesperson said: “The Prime Minister will chair a COBR meeting tomorrow to discuss the situation regarding international travel, in particular the steady flow of freight into and out of the UK.
"Further meetings are happening this evening and tomorrow morning to ensure robust plans are in place.”
The French prime minister’s office said the travel ban would last 48 hours from midnight on Sunday.
The statement said the short two-day period would buy authorities time to find a “common doctrine” on how to deal with the threat. It specified that “flows of people or transport to the UK are not affected”.
Transport Secretary Grant Shapps called on members of the public and hauliers to avoid travelling to Kent ports.
In a tweet,he said: “Following the French government’s announcement it will not accept any passengers arriving from the UK for the next 48hrs, we’re asking the public particularly hauliers not to travel to Kent ports or other routes to France.
“We expect significant disruption in the area."
The Netherlands' ban came into effect on Sunday morning and will last until at least the end of the year, after the government there said it was reacting to tougher measures imposed in London and surrounding areas on Saturday by Prime Minister Boris Johnson.
The Netherlands said it will assess “with other European Union nations the possibilities to contain the import of the virus from the United Kingdom”.
After flights were cancelled earlier on Sunday for at least 24 hours, Eurostar trains between Belgium and the UK have been cancelled from Monday, following the Belgian government’s announcement that borders with the UK will close at midnight.
Shortly after Eurotunnel announced its closure, the Port of Dover said its ferry terminal was closing to all accompanied traffic leaving the UK due to the border restrictions in France.
It added on its website: “Both accompanied freight and passenger customers are asked not to travel to the Port. We understand that the restrictions will be in place for 48 hours from midnight (CET).We apologise for the inconvenience and will provide an update as soon as possible.
The south-east of England has been put under tough new Tier 4 restrictions, in order to curb the spread. The new measures ban people from mixing indoors and outdoors with others, while retail, leisure and hospitality businesses must all close.
“There’s no evidence to suggest it is more lethal or causes more severe illness,” the prime minister stressed, or that vaccines will be less effective against it.
The UK has alerted the World Health Organization (WHO) that the new variant identified this week appears to be accelerating the spread of Covid-19, saying it accounted for some 60% of the capital’s cases.