England's national lockdown has helped to bring coronavirus "back under control" but vigilance is still needed, the health secretary has said.
Matt Hancock hailed the restrictions a success and said infections in England dropped by about 30% in the last week.
The lockdown ends on Wednesday and will be replaced with tiered restrictions.
Mr Hancock stressed the need for the regional system, saying "while we can let up a little, we can't afford to let up a lot".
Speaking at a Downing Street news briefing on Monday, he said people following the lockdown rules meant "we've reduced pressures on the NHS, we've brought down the number of coronavirus cases, we've got this virus back under control."
He added: "The success of our collective efforts means that from Wednesday, everyone in England, even those in tier three, can have some greater freedoms - but we don't have much headroom."
Mr Hancock pointed to a major study from Imperial College London that has suggested that the number of infections has fallen by a third since the lockdown was introduced a month ago.
However, the health secretary called for vigilance and said the country could not risk Covid cases rising again as we head towards Christmas.
Prof Stephen Powis, national medical director of NHS England, told the same briefing that it was "crucial" to have infection rates under control ahead of January, when the NHS is at its busiest.
He said he was "confident people will act sensible over Christmas" - when restrictions are to be relaxed for five days - and the country will go into the new year with the number of infections staying down and falling.
Prof Powis also said that the NHS had "started to turn the corner" as the number of people in hospital with coronavirus is falling, but said it was "critical" that cases remained low.
He said: "We have the evidence that infection rates are now falling and have been falling during this period of lockdown.
"And we are now just beginning to see that translate through into hospital admissions, which have been falling, and into the overall number of people in hospital which in recent days has started to turn the corner, and is now falling."
Mr Hancock pointed to the government's newly-published impact assessment in needing the toughened tiered approach in England, following criticism from some Tory MPs.
He said it "clearly" demonstrated the move was "necessary to avoid a much worse outcome", and called for vigilance.
Asked whether Conservative backbenchers considering voting against the government's proposed new tier system for England during a Commons vote on Tuesday are being irresponsible, Mr Hancock said he urged all MPs to vote for the measures.
He said the tiered system was the "best way to avoid a third lockdown" and the "most proportionate way to take the action that we need to keep people safe, and to stop the NHS being overwhelmed".
Meanwhile, Labour leader Sir Keir Starmer confirmed his party's MPs would be encouraged to abstain from Tuesday's vote - meaning it is likely to pass, even as Tory backbenchers threaten to rebel.
Sir Keir said he remained "deeply concerned that Boris Johnson's government has failed to use this latest lockdown to put a credible health and economic plan in place".
The health secretary repeated the government's earlier pledge to roll out mass community testing in tier three areas, including testing people without symptoms, after the lockdown ends.
Mr Hancock said mass testing had successfully brought down infections in Liverpool - where 300,000 people were tested for Covid-19 - and would give tier three areas a "faster way out of the toughest restrictions".
He appealed to anyone who was offered a test to take one, as "you might just save a life".
However, health leaders have warned that mass testing plans in England threaten to be a "distraction" from other priorities such as the rollout of a vaccine.
Mr Hancock said mass testing and vaccination needed to "run alongside each other", which had already been happening in vaccine trials to find out if people who are vaccinated have caught Covid-19.
Community testing is being seen as a crucial development to get the UK through winter until the vaccines arrive.
This refers to the use of rapid testing to spot asymptomatic cases - people who do not have symptoms.
It is what the government was referring to as the "moonshot" programme a few months ago.
Local authorities are being given access to these tests to try to root out the virus among people who do not know they have it.
It was one of the tools that Liverpool has used over the past month or so during which infection levels have been reduced three-fold.
Councils across the country are likely to offer it to people in neighbourhoods with high infection rates and to target high-risk workplaces like food factories.
Nationally it is being used to test care home visitors and help university students return home for Christmas.
But despite the optimism among ministers, there are words of caution.
These tests were never intended for community use like this.
They may only pick up three quarters of positive cases, dropping to a half if carried out by untrained people.
The government is pushing the boundaries.
That may be understandable in a pandemic, but the effectiveness of this programme is far from certain.
Mass coronavirus testing of students, so they can safely return home for the Christmas break, has already begun at many UK universities.
Mr Hancock urged students to take a test if they are offered one but defended the fact that the scheme is not mandatory.
Meanwhile on Monday, the government recorded another 12,330 daily coronavirus cases and a further 205 deaths within 28 days of a positive test.
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