Video report by ITV News Political Correspondent Libby Wiener
Up to 10,000 people in the UK could already be infected with coronavirus, the government's chief scientific adviser Sir Patrick Vallance has warned.
Speaking at a press conference alongside the prime minister, it was announced the UK would now be moving from the "contain" to "delay" phase in a bid to slow down the spread of Covid-19.
The prime minister also outlined new advice that those with mild coronavirus symptoms should self-isolate for seven days.
Mr Johnson said: "If you have coronavirus symptoms however mild, either a new continuous cough or a high temperature, then you should stay at home for at least seven days to protect others and help slow the spread of the disease.
"We advise all those over 70 with serious medical conditions against going on cruises and we advise against international school trips."
It comes as the number of confirmed coronavirus cases in the UK rose to 590 with two further deaths - bringing the total number of people to have died from the virus to 10.
Under the new measures, the Government is recommending foreign trips be cancelled and says even those with mild symptoms should self-isolate for seven days whether they have travelled to virus-hit countries or not.
ITV News Health Correspondent Emily Morgan provides an update on the coronavirus outbreak in the UK
But medical experts said the UK's plans were "balanced" and "sensible".
Professor Keith Neal, emeritus professor in the epidemiology of infectious diseases at the University of Nottingham, said the plans would help contain the spread of the virus.
He said: "The plans are sensible, it is very easy to say more needs to be done, but there is little evidence to make any decision.
"If people who might have coronavirus (or another virus) self-isolate based on fever and cough then this should limit the spread of the virus. What we know is that people are most infectious during the first week of symptoms.
Appearing to back the Government's decision not to cancel major sporting events yet, Prof Neal said such a measure might lead people to go to pubs or watch games with friends meaning "more significant close contact might occur".
On Thursday night, ITV News Political Correspondent Paul Brand revealed that a third Conservative MP is self-isolating.
In an address at Downing Street, the Government's Chief Scientific Adviser Sir Patrick Vallance warned virus modelling suggests between 5,000 and 10,000 people in the UK currently have Covid-19 but most are unaware they have contracted it.
Sir Patrick said: "Currently we are on a trajectory that looks as though it is about four weeks or so behind Italy and some other countries in Europe.
"There are currently 590 cases that have been identified in the UK and there are more than 20 patients in intensive care units.
"If you calculate what that really means in terms of the total number, it is much more likely that we have between 5,000 and 10,000 people infected at the moment.
"That is still a relatively small number."
Sir Patrick Vallance also warned the UK was around four weeks behind Italy's outbreak, and that the peak number of cases could come within a 10 to 14 week period.
Italy has been the hardest European country hit by the disease, with the total number infected at more than 15,000 and more than 1,000 deaths.
Mr Johnson said families would continue to "lose loved ones before their time" as the coronavirus outbreak worsens.
"We've all got to be clear, this is the worst public health crisis for a generation," said the PM.
"Some people compare it to seasonal flu, alas that is not right.
"Due to the lack of immunity this disease is more dangerous.
"It is going to spread further and I must level with you, I must level with the British public: many more families are going to lose loved ones before their time."
Under the "delay phase" measures schools will not close but Boris Johnson said the Government is considering banning mass events.
The prime minister said the Government would not yet ban major sports events, but that the measure was under consideration to help alleviate the strain on public services.
He added proposed measures are more effective than school closures or cancelling mass gatherings and suggested the plans could delay the outbreak by two to three weeks.
The Government has come under criticism in some quarters for its apparent reluctance to shut schools and stop mass gatherings.
However the prime minister fired back at the accusations, adding he was following the scientific advice on the matter and that introducing "draconian" measures too early would not help stop the spread of the disease.
Video report by ITV News Political Correspondent Paul Brand
What does the delay phase actually entail?
He said: "You need to make sure that you move that period where we're asking older people, vulnerable people, to go through a pretty difficult period of isolation and we time it so as to coincide with the moment when they are at most risk of exposure to the illness.
"That's one of the reasons why we are not triggering that draconian measure now."
Mr Johnson also warned that the Covid-19 advice is likely to be expanded in the coming weeks.
"At some point in the next few weeks we are likely to go further and if someone in a household has those symptoms then we will be asking everyone in that household will stay at home," he said.
That measure is not being advised yet the PM said, but he added: "I want to signal now that this is coming down the track."
On a day where the FTSE 100 fell by more than 10 per cent, BT Group's chief executive Philip Jansen became the first director of the UK's top 100 firms to test positive for coronavirus.
He is now self-isolating as advised by Public Health England.
In a statement, Mr Jansen said: "Having felt slightly unwell I decided as a precaution to be tested. As soon as the test results were known I isolated myself at home."
A statement from Imperial College Healthcare NHS Trust said an 89-year-old patient who was "very unwell with underlying health conditions" had died at Charing Cross Hospital after testing positive for the virus.
Tony Chambers, interim chief executive, Barking, Havering and Redbridge University Hospitals NHS Trust, said another patient - "in her sixties" - had died at Queen's hospital.
He said: "She had been very unwell with significant other health conditions.
"Our thoughts and condolences are with the patient's family at what is undoubtedly a very distressing time."
Coronavirus: Everything you need to know
The latest figures for coronavirus cases include 24 new cases in Scotland where the number of people confirmed to have the virus almost doubled from 36 to 60.
At First Minister's Questions on Thursday, Ms Sturgeon said it would be "inappropriate that we continue as normal".
Dr Robin Howe, incident director for the Covid-19 outbreak response at Public Health Wales, said two of the cases had no history of travel coronavirus-affected countries and are not known to have had contact with any other confirmed cases.