Up to 10,000 people in the UK probably have coronavirus, officials have said, as they announced they were stepping up Britain’s response to the outbreak with new actions designed to delay its spread.

Anyone showing cold or flu-like symptoms is being told to isolate themselves for seven days from Friday onwards – a measure brought forward by at least a week.

They should then stay at least two metres, or “about three steps”, away from anyone else, sleep alone and ask for help “to get the things you need”.

“Stay away from vulnerable individuals such as the elderly and those with underlying health conditions as much as possible,” the new advice reads.

Schools have been ordered to cancel all foreign trips, and elderly people or those with underlying health conditions are advised not to go on cruise ships. However, ministers have stepped back from immediate closures and sporting events will still go ahead, with fans allowed into stadiums.

Patrick Vallance, the government’s chief scientific adviser, said the true number of infections was “likely” to be between 5,000 and 10,000 – many times higher than the current figure of 590.

“We are in a period when we have got some, but it hasn’t yet taken off,” he told a press conference.

The warning came as Boris Johnson sought to prepare the public for tougher times to come, saying: “This is the worst public health crisis for a generation.”

He dismissed comparisons to seasonal flu: “Because of the lack of immunity, this disease is more dangerous and it’s going to spread further.

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“Many more families are going to lose loved ones before their time.”

Explaining the decision not to move to more draconian restrictions now, unlike almost all neighbouring countries, Mr Johnson said: “The most dangerous period is not now but some weeks away, depending on how fast it spreads.

He hinted at a likely shift to banning fans from sporting events, saying: “We are not saying ‘No’ to that sort of measure, of course not – we are keeping it up our sleeve.”

Nevertheless, he insisted: “There is very little epidemiological or medical reason, at the moment, to ban such events.”

Prof Vallance, who said the UK was about four weeks behind Italy – the worst-hit country in Europe in terms of the progress of its outbreak – was scornful about the option of a flight ban of the kind imposed by the US president, Donald Trump.

A blanket ban on flights from China and the imposition of screening at airports at the start of the outbreak might have won the UK a day or two, he said. But, he added: “It’s certainly too late now... These things sound great, but don’t always work.”

Chris Whitty, the chief medical officer, declined to say how high the death toll might reach, after earlier announcing that the number of fatalities had reached 10. More than 20 people are currently in intensive care.

He said it was possible that up to 80 per cent of the UK population would catch the virus – and that 1 per cent of the infected population could die – but said this was “entirely speculative”.

He added: “We think that the peak may be something like 10 to 14 weeks away – it may be a bit longer.”

Mr Johnson dismissed any fears about his own health, as someone who must meet many other people, saying: “I’m washing my hands – that’s the crucial thing.”

Under the new “delay” stage of the official response, individuals who experience a new and persistent cough or a raised temperature are asked to stay at home for seven days – covering the three-to-four day period when coronavirus is most infectious.

Crucially, experts say that self-isolation should be carried out even if a person with cold or flu-like symptoms does not have a temperature, as this is absent in as many as 40 per cent of cases of the coronavirus.

Chris Whitty, Boris Johnson and Patrick Vallance address a press conference in 10 Downing Street (Simon Dawson/PA)

Those staying at home are urged not to call NHS 111 or 999 or seek a coronavirus test unless their condition deteriorates, in order to avoid clogging up healthcare facilities needed by others. Most are likely to experience only mild symptoms and may recover full health without ever learning whether they actually had the coronavirus.

At a later stage, when the number of cases starts to rise more dramatically and the virus is widespread in the population, Mr Johnson made clear that new advice will be issued requiring whole households to remain at home for two weeks if any of their members has the infection.

Efforts will also be made at this stage to keep vulnerable and elderly people away from contact with other people to the greatest extent possible, in order to protect those for whom it is most likely to be fatal. This measure is thought to be capable of cutting the death rate by as much as 30 per cent, but the authorities do not intend to introduce it at too early a stage for fear of increasing loneliness and stress among the elderly.

Once the virus is widespread, it is likely to become necessary for the NHS to cancel non-urgent operations to free up beds and doctors for severe coronavirus cases, and talks are already under way within the health service to prepare for this step.

There are no plans to shut down parliament or essential public services, with officials saying it is necessary to keep the country running during the outbreak.

The medical and scientific advisers are steering ministers away from following Ireland in shutting down schools, warning that children would only congregate elsewhere during an enforced school break, and would probably end up spending time with grandparents who are far more at risk than them.

Measures undertaken during the so-called “contain” phase of the strategy, which included testing of anyone showing symptoms, will now be wound down. Experts believe that these actions – coupled with the continuing advice on washing hands – have already reduced the expected peak of the disease by as much as 20 per cent and have delayed it by two or three weeks.