Boris Johnson has said the government will start offering vaccination appointments 24-hours a day seven days a week “as soon as we can”.
Downing Street had said earlier this week there was no “clamour” from people to be vaccinated round the clock.
Speaking during PMQs on Wednesday, Johnson said more details about 24/7 vaccine centres would be set out by health secretary Matt Hancock “in due course”.
It comes as AstraZeneca said it would be able to supply two million doses of its vaccine, developed in Oxford, to the UK every week by mid-February.
With rolling out the vaccines key to easing lockdowns, the latest NHS figures showed 2,431,648 in the UK have received a first dose.
But the health service was under extraordinary pressure with the number of Covid-19 patients in hospital in England at a record 32,202 as of 8am on Tuesday — up 22% on a week ago, and 82% since Christmas Day.
NHS Providers chief executive Chris Hopson told MPs the peak demand on the health service may not be reached until early to mid-February.
Latest figures showed that as of Tuesday, a further 1,243 people in the UK had died within 28 days of testing positive for Covid-19, with a further 45,533 cases being confirmed by labs.
The government has warned the current national lockdown in England will be made even stricter if the public do not follow the rules.
Hancock said on Wednesday morning he restrictions will remain in place for as “long as they are necessary”.
The health secretary told people not to “take the mickey” out of the restrictions, but said it was “impossible to know” when they could be eased.
But Keir Starmer, the Labour leader, questioned accused the government of being “so slow to act” when infection rates began to surge in December.