The prime minister will chair a meeting of the government’s emergency committee later after France closed its border with the UK for 48 hours.
The move, announced on Sunday, means no lorries or ferry passengers will be able to sail from the port of Dover.
France said the action was necessary because of the prevalence of a new variant of coronavirus in the UK.
Nations including Germany, Italy, Belgium, the Irish Republic, Turkey and Canada are suspending UK flights.
Switzerland has also suspended UK flights, and Hong Kong will do so from midnight.
Austria is also set to bring in a ban, while Bulgaria has suspended flights to and from the UK from midnight. Unlike the short-term measures in many other nations, its ban lasts until 31 January.
European Union member states are due to meet in Brussels to discuss a co-ordinated response.
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, the government pledged to provide refunds for rail and coach tickets bought for the Christmas travel window between 23 – 27 December, after millions of people across the UK saw their festive plans severely restricted or scrapped.
Transport Secretary Grant Shapps said this would apply to journeys in England booked on or after 24 November, when the Christmas travel window was announced.
Mr Shapps said: “This ensures no one is left out of pocket for doing the right thing – staying home in tier four, and elsewhere staying local and only meeting your Christmas bubble on Christmas Day.”