There is “no question whatsoever” of the UK reopening the “fundamental tenets” of Boris Johnson's deal, he said.
“I don’t recognise this story at all," Steve Barclay said.
Minister blames an "impossible situation" after holidaymakers escape measure to prevent spread of more contagious Covid-19 variant.
Major Hugh Lindsay died in an avalanche in Switzerland during a skiing trip with Prince Charles.
Transport secretary Grant Shapps announced that travellers arriving in England from those countries after 4am on Saturday will need to self-isolate for 14 days.
And Switzerland could be next on the UK's list.
Scotland also adds Switzerland to list north of border amid a spike in Covid-19 cases abroad.