Lockdown restrictions could be lifted from early March, with a return to the tier system for controlling Covid-19, the vaccines minister has said.
Nadhim Zahawi said that once millions of the most vulnerable are vaccinated with a first dose by the middle of February, it takes just a few weeks for their immune response to kick in and offer protection.
It comes as the total number of people to receive a first vaccine dose in England, Wales, Scotland reached 3.94 million.
The Government is currently on track to vaccinate 15 million people across the UK by mid-February, including health and social care staff, the elderly and people in care homes.
Mr Zahawi told BBC Breakfast: "If we take the mid-February target, two weeks after that you get your protection pretty much for the Pfizer BioNTech (jab), three weeks for the Oxford AstraZeneca, (then) you are protected.
"That's 80% of mortality.
"One of the things that we don't know yet – and the deputy chief medical officer Jonathan Van Tam is on record as saying 'look give me a couple of months and I'll tell you' – is the impact of the vaccine on transmission rates, ie infecting people.
"So, that will become apparent. So there are a number of caveats that, obviously, stand in the way of us reopening the economy.
"It will be gradual, it will be probably through the tiered system, but you're looking at that sort of period – two to three weeks after the middle of February where we've protected those top four cohorts."
Mr Zahawi told Times Radio that by the "first (or) second week of March" there should be "very clear evidence of a sort of a break in the correlation between infection rates and hospitalisation and obviously death".
He added: "But of course, there are a lot of unknowns, we don't know the impact on transmission of the vaccines yet.
"There are lots of caveats on this so I don't want to sort of over-promise and under-deliver on this."
Asked if there was a role for mass testing, Mr Zahawi said the combination of vaccination and mass testing would allow the economy to gradually reopen.
And on the question of schools going back in early March, he said: "I'm saying to you that there are lots of uncertainties, we still don't know what the impact of the vaccines are on transmission... but they (schools) are top of our list in terms of wanting them to reopen as soon as practically possible, with a combination of testing and, of course, vaccination as well."
It comes as:
– New data analysed by the PA news agency shows that of the 315 local areas in England, 36 (11%) have seen a rise in case rates in the seven days to January 13 compared with the previous week while 279 (89%) have seen a fall. All areas in the top 10 have seen a week-on-week drop, with only three areas in the top 50 seeing an increase in rates.
– Knowsley in Merseyside has the highest rate in England, with 1,853 new cases recorded in the seven days to January 13 – the equivalent of 1,228.3 cases per 100,000 people. Barking and Dagenham in London has the second highest rate.
– Wales' First Minister Mark Drakeford told BBC Radio 4's Today programme things are "improving slowly" there. But he said: "I think it will be certainly the middle of February before we begin to see any more significant lifting of the lockdown."
Speaking on Monday, the national medical director for NHS England, Professor Stephen Powis, told Good Morning Britain that the vaccination programme will not have an impact on hospital admissions or death rates until "well into February".
He said infection rates in London had "slowed down" but there was "less of a slowdown" in the rest of the country, adding: "For the next few weeks and into February, it's really important that everybody sticks to those social distancing guidelines."
Meanwhile, the chief executive of the NHS Confederation warned that the health service could hit the limit of its critical care beds this week as hospital admissions due to Covid-19 continue to rise.
Speaking to Times Radio, Danny Mortimer praised the determination of critical care staff in tackling the surge in cases, saying: "I think one of the most remarkable things is that our teams have kept going throughout that (winter) period.
"And they refuse to see a point where they aren't prepared to keep on going anymore."
But he warned: "I think this next week, we will be at the limit of what we probably have the physical space and the people to safely do.
"And, of course, this is the week when we expect also the highest rate of admissions, the highest demand for the care that we're providing."
Mr Mortimer said the NHS now has 5,500 critical care beds, up from 4,000 a year ago, with several hundred more due to become available on Monday.
"That's a sign of both the numbers of people that are coming through, but (also) how really, really ill, how much care and attention, how much help with their breathing, how much damage has been done to people's internal organs," he said.
Elsewhere, all eligible care home residents in Newcastle and most of the staff looking after them have received a coronavirus vaccine, Dr Jane Carman, clinical director of Inner West Primary Care Network, has said.
She said planning, communication and teamwork were key to getting the Pfizer vaccine out to more than 50 care homes in the city, giving jabs to almost 2,000 residents.
Across the UK, millions of over-70s and the clinically extremely vulnerable can expect to start being invited for a vaccine as the Government expands rollout of the jabs.
More than 3.8 million people in the UK – including over-80s, care home residents, and NHS and social care staff – have already received their first dose of a Covid-19 vaccine, but from Monday it will be rolled out to the next two priority groups.
The Government said it would remain the priority to vaccinate those in the first two groups, but that sites which have enough supply and capacity to vaccinate more people will be allowed to offer jabs to the next cohorts.
Ten further mass vaccination centres are opening in England from Monday, including Blackburn Cathedral, St Helens rugby ground, Norwich Food Court and a park-and-ride outside York.
NHS England said they will join the seven existing mass vaccination sites across the country, alongside around 1,000 GP-led surgeries and more than 250 hospitals already providing jabs.
Elsewhere in the UK, more people are now in hospital with coronavirus in Scotland than at any time during the pandemic – despite new infections falling to the lowest level in almost three weeks.