The prime minister made the remarks after Britain on Thursday banned arrivals from South America, Portugal and some other countries over fears about a strain of the virus detected in Brazil.
The new rules will be in place until at least Feb. 15, he said.
Meanwhile, Johnson said 3.2 million people across Britain have received vaccines.
The pressures on the National Health Service (NHS) are "extraordinary" and it would be "fatal" to show complacency now, he said.
"This is not the time for the slightest relaxation of our national resolve," Johnson said, urging the public to stay at home.
England is currently under the third national lockdown since the outbreak of the pandemic in the country. Similar restriction measures are also in place in Scotland, Wales and Northern Ireland.
Another 55,761 people in Britain have tested positive for COVID-19, bringing the total number of coronavirus cases in the country to 3,316,019, according to official figures released Friday.
Another 1,280 have died within 28 days of a positive test. The total number of coronavirus-related deaths in Britain now stands at 87,295, the data showed.