In a statement, the company said: "Due to the French and Belgium government's announcements that borders with the United Kingdom will close at midnight, we are unable to run any trains from London to Paris, Brussels or Amsterdam on Monday".
A travel ban will remain in place until January 1, the government said in a statement early Sunday, adding that it is monitoring developments and is considering additional measures regarding other modes of transport.
As the World Health Organisation urged its European members to strengthen measures against a new variant of COVID-19 circulating in Britain, European nations including Germany, Ireland, Italy, Austria, Romania, the Netherlands and Belgium said they were moving to block air travel.
Johnson had said the new strain "may be up to 70% more transmissible than the old variant" although there was no evidence it was more deadly or led to a more severe illness.
The flight cancellations and tightening of Covid-19 restrictions prompted a rush of last-minute bookings on Eurostar on Sunday.
The ministry said a case study in the Netherlands "at the beginning of December revealed a virus with the variant described" in the UK.
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Vivek Murthy said the most important thing is that individuals reduce the spread of the virus by following public health advice about facial masks, hand-washing and social distancing.
"There are a great many questions about this new mutation and if it is not already on the mainland", he said.
People forced to abandon trips because of new tier restrictions will only be offered a voucher or to switch their flight to a different flight.
The number of coronavirus cases in Britain surged by 35,928 on Sunday, the highest daily rise since the start of the pandemic, and it recorded 326 deaths, taking the official toll to more than 67,000.
Austria's health ministry told the APA news agency that it would also impose a flight ban, the details of which were still being worked out.
British Health Secretary Matt Hancock told the BBC Sunday that "the new variant is out of control". No mixing of households is now allowed indoors in Tier 4 areas, including London, and only essential travel is permitted into and out of such areas. Train stations in London on Saturday night filled with crowds of people scrambling to leave the city.
"Is it doable? Yes, I think we can do it, but [what] we've got to do is prepare and be ready to execute", Murthy said, shifting the focus to being ready to deliver the vaccine.