Flights from the UK are being suspended to territories 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 said he spoke with French President Emmanuel Macron and both sides wanted to resolve "these problems as fast as possible".
Countries to impose a ban on UK arrivals include Belgium, Canada, Germany, Ireland, Italy, Portugal, Romania, Russia, and Switzerland.
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.
More about: UK coronavirus
