The government's plan to move England out of lockdown will be "cautious but irreversible", Boris Johnson has said.
The prime minister is due to set out the roadmap for ending restrictions next Monday.
He told reporters the plan would include target dates for changes "if we possibly can", but he warned high rates of infection could lead to delays.
It comes as a group of Tory MPs call for a commitment to a "free life" and ending of lockdown measures before May.
Senior backbencher Steve Baker said he wants the prime minister to "let us reclaim our lives, once and for all".
The PM is likely to be questioned about his plans later when he hosts a Downing Street press conference at 17:00 GMT - alongside England's Chief Medical Officer, Chris Whitty, and the chief executive of NHS England, Simon Stevens.
On Sunday, the government said it met its target to offer a vaccine to the 15 million most vulnerable people across the UK.
Figures on Monday showed a 29% drop in the number of positive cases across the country, down to 9,765 - the lowest figure since 2 October.
But there are still concerns over the numbers, with over 88,000 cases recorded in the last week - an average of 157 cases per 100,000 - and 4,598 people dying within 28 days of testing positive for the virus.
Labour said the government must "lock in the gains of the vaccine" and ensure more measures were introduced to reduce the spread of the virus - such as financial support for self-isolation and updated workplace guidance.
Mr Johnson and senior members of his cabinet are set to spend the week looking into the latest coronavirus statistics before making an announcement on its plans.
He said: "The dates that we'll be setting out will be the dates by which we hope we can do something at the earliest."
There has been a raft of speculation on the date of re-openings of businesses and hospitality - much of which has been dismissed by Downing Street.
But sources in No 10 told the BBC they were increasingly confident pupils in England would return to school on 8 March - the earliest the PM said the move could happen.
'Keep looking at the data'
Mr Johnson said no decisions had been taken yet, but the March date for schools had "for a long time been a priority of the government and families up and down the country".
He added: "We will do everything we can to make that happen, but we have got to keep looking at the data.
"There are still 23,000 or so Covid patients in the NHS - more than at the April peak last year - there are still sadly too many people dying of this disease; and rates of infection, although they are coming down, are still comparatively high.
"So we have got to be very prudent and what we want to see is progress that is cautious but irreversible. I think that is what the public, people up and down the country, want to see."
Over the weekend, 63 Tory MPs wrote to Mr Johnson, calling for easing to begin in March and for analysis to be released justifying any measures staying in place.
Mr Baker, who is the deputy chair of the lockdown-sceptic Covid Research Group (CRG) of Tory MPs leading the call, said schools should return on 8 March, hospitality should re-open by Easter and all other elements should be back to normal by 1 May - when all people in the top nine priority groups have been offered a vaccine.
The proposal was rejected by Foreign Secretary Dominic Raab, who told the BBC's Andrew Marr on Sunday that the government would be "cautious".
But writing in the Telegraph, Mr Baker reasserted his plan, saying: "As the prime minister said, let us reclaim our lives, once and for all. This can be a moment of unity - for our country and the Conservative Party - as we look ahead with confidence, hope and optimism to a much brighter future."
Fellow CRG member and Tory MP Jackie Doyle-Price said the government "have to think about livelihoods", telling BBC Radio Essex: "The moment you open schools up then there is no excuse for not opening up the rest of the economy."
'Reunite and celebrate'
Hospitality bosses are asking the government to reopen pubs by April, with the chairman of Wetherspoon warning the industry is "on its knees" and jobs are on the line.
The plea comes after industry figures showed the plight the sector is facing, with a net loss of almost 6,000 licensed premises last year - triple the tally in 2019.
More than a dozen MPs have also called on Mr Johnson to allow restricted weddings to return from 8 March, followed by restriction-free weddings from 1 May.
Tory former minister Esther McVey said after the top nine groups of people are vaccinated, it should be "a huge moment for the UK to hold its head up high, for couples to walk down the aisle, and for families up and down the country to reunite, to celebrate and to plan their futures".
Any broad political consensus that existed in the early days of this pandemic has long gone.
The Tory MPs that make up the Covid Recovery Group have been increasingly critical of prolonged restrictions.
This is a group containing some senior Conservatives who are willing to be vocal, and willing to exert pressure on the prime minister. Their stance will no doubt be a factor in Downing Street's thinking.
But it would be wrong to assume lockdown scepticism is representative of everyone on the Tory benches. Of more than 360 Conservative MPs, 63 signed the latest letter to Boris Johnson urging an easing of restrictions as soon as possible. That's not an inconsiderable number.
However, there are also Tory MPs that advocate a more cautious approach, as do plenty on the opposition benches.
The pressure from some in his party to move quickly out of lockdown creates tricky political tension for the prime minister - but it's not necessarily a majority view.
Another senior Tory backbencher, Robert Halfon, said the PM needed to "provide some kind of optimism to the public" over lockdown easing, but warned against people relaxing too soon.
The chair of the Education Select Committee told BBC Radio 4's Westminster Hour: "I understand where [the Covid Recovery Group] are coming from and my heart has a lot of sympathy.
"I just don't want a repetition of what went on last year where we thought we were over the worst and then we're suddenly back in tiers of lockdown."
Meanwhile, Welsh Health Minister Vaughan Gething said he would not want to give a "cast iron guarantee" about future lockdowns.
He said: "The danger is we try to set out absolutes - with talk of whether this is irreversible, or whether nothing else will happen in the future.
"What we want to do is make choices based on the best available data and information, to see case rates driven as low as possible, and then to have a cautious exit out of the current lockdown we're in."