The World Health Organisation urged Europe to increase its Covid-19 response and said that faster-spreading new strains were crunch time for the pandemic.
The British mutation and another that emerged in South Africa have wreaked havoc in those nations since late last year.
The majority of new cases in the UK were from the new variants.
WHO Europe director Hans Kluge said the current situation was “a tipping point in the course of the pandemic” and the continent needed to strengthen social-distancing measures.
“Without increased control to slow its spread, there will be an increased impact on already stressed and pressured health facilities,” he said.
Helge Braun, an ally of German Chancellor Angela Merkel, said the country's lockdown might need to be extended in light of the mutant variant, while French Health Minister Agnes Buzyn said it was unlikely the continent would be able to keep the British strain at bay.
However, Spanish health chief Salvador Illa ruled out another lockdown, despite acknowledging the “upward trend” in positive cases and deaths.
UK Prime Minister Boris Johnson was set to announce an expansion of the country’s vaccination campaign, with the British Army drafted in to help.
About 1.3 million people in Britain have been inoculated but the government faces a challenge to hit its target of 14 million by mid-February.
Doctors on Thursday said that some patients were turning down the US-German designed Pfizer/BioNTech shot in favour of the British-made Oxford/AstraZeneca vaccine.
Paul Williams, a former Labour MP who is a practising doctor, said some of his patients would “wait for the English one”.
"People at risk of death in the depths of a pandemic," he said on Twitter. "A lesson that nationalism has consequences."
A briefing leaked to the Health Services Journal suggested London's hospitals were on the brink of being overwhelmed.
Even in a relatively positive scenario, the capital’s hospitals could be beyond capacity in less than a fortnight, the journal reported.
The UK on Thursday reported more than 52,000 new cases and 1,162 deaths in 24 hours, with more than 30,000 people in British hospitals with the virus, the highest number since the pandemic began.
Chris Hopson, head of NHS Providers, said hospital chiefs were considering transferring some inpatients to care homes.
"We've seen 5,000 new patients in hospital beds with Covid-19 over the past week – that's 10 full hospitals' worth of Covid patients,” he said.
Home Secretary Priti Patel warned people that police powers had been extended to better enforce England's third national lockdown, with officers stopping people in the street to ask where they are going.
“The message right now is stay at home,” Ms Patel told the BBC.
