Visiting a north London hospital as some of the first patients received doses of the Oxford/Astra Zeneca vaccine, prime minister Boris Johnson said tougher restrictions were inevitable.
'If you look at the numbers there is no question that we are going to have to take tougher measures and we will be announcing those in due course,' Mr Johnson said.
Scottish first minister Nicola Sturgeon, meanwhile, has announced a lockdown from midnight - with schools across Scotland to remain closed until February at the earliest.
Labour leader Sir Keir Starmer on Sunday called for a full national lockdown in England within 24 hours, and groups including the Doctors Association UK have joined calls for an emergency national lockdown.
Former health secretary Jeremy Hunt - now chair of the influential House of Commons health select committee - warned that although during his record tenure in the role the NHS had faced four 'serious winter crises', soaring rates of COVID-19 infection in the second wave of the pandemic meant pressure on the health service was now 'off-the-scale worse than any of those'.
Mr Hunt called for immediate closure of schools, borders and a ban on all household mixing.
Time to act: thread on why we need to close schools, borders, and ban all household mixing RIGHT AWAY.— Jeremy Hunt (@Jeremy_Hunt) January 4, 2021
Calls for rapid action to contain the COVID-19 pandemic came after the UK recorded more than 50,000 new infections per day for six days in a row.
COVID-19 cases rising
More than 75,000 people in the UK have died within 28 days of a positive COVID-19 test, and on 28 December 23,823 were in hospital with the virus - more than the number at the peak of the first wave.
DAUK vice chair Dr Natalie Ashburner said: 'We acknowledge that these decisions are far from easy to make but the rapid of acceleration of the virus is deeply concerning and the current measures don’t appear to be containing transmission of the virus.
'For the sixth day in a row over 50,000 transmissions have been recorded and the death toll is climbing inexorably. DAUK is particularly worried that things will get even worse as the effects of Christmas and New Year are fully realised.'
Dr Zainab Najim of the DAUK GP committee said: 'We are in the midst of the toughest winter the NHS has ever seen, exacerbated by the new highly transmissible strain of COVID-19.
'Sickness rates among NHS staff have doubled to trebled compared to last winter and there are real worries that safe patient care could be compromised by the sheer number of patients needing care and staffing ratios not seen in peacetime.'