Bars and restaurants should stay shut until May, researchers have suggested as Boris Johnson acknowledged it was "too early to say" when lockdown measures could be eased.
As 1,290 further deaths were reported, experts modelling the pandemic suggested there could be a huge surge in cases if restrictions were lifted too early.
With the NHS vaccinating at a rate of 200 jabs a minute, the Prime Minister is under pressure to commit to lifting the lockdown in England as soon as the most vulnerable are protected.
But experts warned that early March – when the 15 million priority patients will have received protection from their first jab – would be too soon to lift curbs on freedoms.
And even by the end of April, when all over-50s are expected to have been vaccinated, they said it would be dangerous for a wholesale easing of restrictions.
The Prime Minister, asked whether the lockdown would continue until the summer, said it was "too early to say when we'll be able to lift some of the restrictions", pointing out that there were "unquestionably going to be a tough few weeks ahead".
Downing Street also refused to commit to reopening England's schools by Easter after Education Secretary Gavin Williamson said he would "certainly hope" that would be the case.
The Government's caution in announcing a timetable to ease the lockdown has caused alarm among some Tory backbenchers.
Former chief whip Mark Harper, leader of the Covid Research Group of lockdown sceptics, said: "Once the top four risk groups have been vaccinated and fully protected by March 8 – assuming the Government hits the February 15 deadline – the Government must start easing the restrictions.
"Vaccinations will of course bring immunity from Covid, but they must bring immunity from lockdowns and restrictions too."
But Dr Marc Baguelin, from Imperial College London, who sits on the Scientific Pandemic Influenza Group on Modelling (SPI-M) which advises the Government, said the opening of the hospitality sector before May would lead to another "bump" in transmission.
On BBC Radio 4's World At One he said it would result in "another wave of some extent" and "at best you will keep on having very, very unsustainable level of pressure on the NHS".
Experts from Edinburgh University modelling the impact of the pandemic pointed out that even if 90% of people were vaccinated that still left 10% without protection.
With little known about what impact the vaccine will have on transmission of the virus – and the risk of long Covid in younger people – they suggested that lockdown restrictions should only be lifted slowly, with scenarios modelling what would happen if restrictions continued through until the winter.
Releasing all measures at the end of April – once all the first phase of the vaccination programme covering over-50s, those in high-risk groups and frontline health and social workers are expected to have received a jab – could still lead to a huge surge in cases, they said.
Mark Woolhouse, professor of infectious disease epidemiology at the University of Edinburgh, told the PA news agency: "A gradual relaxing of restrictions hopefully from about the time that the phase one rollout is finished, is much more likely to keep the pressure off the NHS than any wholesale relaxation."
A separate study from the University of Warwick also modelled possible scenarios.
Matt Keeling, professor of populations and disease at the university, said one scenario the model considered was the complete relaxation of all control measures in April when there has been three months of vaccination and 30 million doses.
"Completely stopping all controls is disastrous, we get massive peaks of both daily deaths and hospital admissions," he said.
While he acknowledged that no-one was suggesting that relaxing all measures immediately was a viable strategy, "it just shows that even at that point, you can't relax, even at 30 million doses".
Official figures up to January 20 showed 4,973,248 people had received a first dose of vaccine, an increase of 363,508 from the previous day.
Based on the latest figures, an average of 401,070 people a day will need to be vaccinated to meet the target of reaching the 15 million highest priority cases by February 15.
The Government also said that, as of 9am on Thursday, there had been a further 37,892 lab-confirmed cases of coronavirus in the UK, bringing the total number to 3,543,646.
Professor Anthony Harnden, deputy chairman of the Joint Committee on Vaccination and Immunisation (JCVI), told the BBC the lockdown should continue until the late spring.
He said: "Immunisation is the way out, but it's not at the moment a quick fix and people ought to realise that once they've been immunised they are not 100% protected, and therefore they are not invincible."
In other developments:
– Home Secretary Priti Patel announced a new £800 fine for people who attend house parties with more than 15 people.
– NHS England regional medical director for London Dr Vin Diwakar said breaking lockdown rules was "like switching on a light in the middle of the blackout in the Blitz".
– Northern Ireland's coronavirus lockdown is to be extended for a further four weeks to March 5.
– England's deputy chief medical officer Professor Jonathan Van-Tam said he was delighted that his 79-year-old mother Elizabeth had "some protection against this deadly virus" after she had her Covid-19 vaccination.
The prospect of pubs being forced to shut until May led to warnings that many may not reopen.
Emma McClarkin, chief executive of the British Beer and Pub Association, said: "The Government has a duty to tell publicans when it plans to let them reopen with a clear roadmap alongside the vaccination programme.
"If it won't be until May then it needs to extend financial support for them to survive and to brewers whose businesses also face jeopardy."