Boris Johnson has told the nation he is "absolutely confident that we can send coronavirus packing in this country" and the tide can be turned within the next 12 weeks.
The Prime Minister urged the public to heed advice to keep up social distancing and stay at home if ill or if somebody in their household is ill as he said: "I know it's tough, I know it's difficult... but please, please follow the advice."
He thanked everyone for the "huge efforts that the country is making" and urged businesses to stand by their employees, with further announcements due from Chancellor Rishi Sunak today.
But he stressed that "nothing is ruled out", suggesting tougher restrictions on movement could be introduced if people failed to comply with advice.
"I'm conscious as the days have gone by that people will want to know how long we're expecting them to keep it up," he told reporters at his daily press conference in Downing Street.
"I think, looking at it all, that we can turn the tide within the next 12 weeks and I'm absolutely confident that we can send coronavirus packing in this country.
"But only if we all take the steps that we've outlined, that is vital, that's how we're going to reduce the peak and once we've achieved that and I think that we will, if we take the steps I've said, then the scientific progress that we've been making will really start coming into play."
It comes as the Queen issued a message to the nation which said the UK is "entering a period of great concern and uncertainty", adding that "our nation's history has been forged by people and communities coming together to work as one".
Meanwhile, the death toll in Italy rose to 3,405, overtaking the total number of deaths so far registered in China.
In the UK, the death toll reached 144 as of yesterday, with around four in 10 of all deaths so far in London.
Some 56 of the total deaths have been recorded in the capital, according to calculations by the PA news agency, with the next highest total in the West Midlands (27).
Mr Johnson told reporters that British experts expect to start trials for a vaccine against Covid-19 within a month, although expectations are that a vaccine will take at least a year.
He added: "To give you an idea of what is coming down the track, we're in negotiations today to buy a so-called antibody test, as simple as a pregnancy test, which can tell whether you have had the disease and it's early days, but if it works as its proponents claim, then we will buy literally hundreds of thousands of these kits as soon as practicable."
He said knowing whether you have had Covid-19 could be a "total game-changer" as it would mean those people could get back to work and a normal routine.
Mr Johnson said: "By the same token we're massively increasing the testing to see whether you have it now and ramping up daily testing from 5,000 a day, to 10,000 to 25,000 and then up at 250,000."
He said the "combination of ruthless, determined, collective action and scientific progress" could save "many, many thousands of lives". But he said he couldn't guarantee that by the end of June the peak would be on a "downward slope", although he promised restrictive measures "would be finite".
He said: "Now I cannot stand here and tell you that by the end of June that we will be on the downward slope. It's possible but I simply can't say that that's for certain, of course not, we don't know where we are, and we don't know how long this thing will go on for.
"But what I can say is that this is going to be finite, we will turn the tide, and I can see how to do it within the next 12 weeks."