The disease has already forced the postponement or cancellation of a number of events across the world of sport, with fears growing for this summer's Tokyo Olympics.
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The event was supposed to take place in Tignes, France but organisers have now sought to cancel it after consulting the British and French governments for advice.
Vicky Gosling OBE, Chief Executive Officer of GB Snowsport, said: "GB Snowsport will not put anyone at risk during these times of heightened health concerns and therefore we have taken the sensible and difficult decision to cancel the British Alpine Championships 2020.
"The annual event is a great celebration of British alpine skiing and a real highlight in the GB Snowsport calendar. I want to extend my thanks to all those who had worked so hard in planning the event and for the community of Tignes for their continued support.
"We know this is hugely disappointing for all those who had been looking forward to Tignes but GB Snowsport take their responsibility for the well-being of all athletes, officials and spectators extremely seriously.
"Sadly, due to the continuing threat of the COVID-19 virus and the fact that there are no later dates available in the calendar, the Championships will have to be cancelled for 2020."