Germany, France and Italy are among those to suspend flights from the UK. Outbound train services through the Channel Tunnel have also been halted.
Canada is also blocking UK flights.
Health officials say the new variant is up to 70% more transmissible, but there is no evidence that it is more deadly.
There is also no evidence to suggest that it reacts differently to vaccines.
UK Health Secretary Matt Hancock said the new variant was "getting out of control" while Denmark, Italy and the Netherlands announced they had already detected it.
The European Council meeting of government representatives is expected to take place at 10:00 GMT. The speed at which governments have announced their bans on travellers from the UK shows the scale of the alarm, the BBC's Gavin Lee in Brussels reports.
Also on Monday, the European Medicines Agency is expected to approve the Pfizer-BioNTech coronavirus vaccine that is already being administered in the UK and in the US under emergency approval.
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