He said people should work from home where possible, as part of a range of stringent new measures.
Pregnant women, people over the age of 70 and those with certain health conditions should consider the advice “particularly important”, he said.
People in at-risk groups will be asked within days, possibly by this weekend, to stay at home for 12 weeks.
The number of people who have died in the UK has now hit 96 after the first person in Wales has died of the the condition.
In the first of a series of daily briefings on the virus, which causes the Covid-19 disease, Mr Johnson said “drastic action” was needed as the UK approaches “the fast growth part of the upward curve” in the number of cases.
Mr Johnson said that by next weekend, those with the most serious health conditions must be “largely shielded from social contact for around 12 weeks”.
Sir Patrick Vallance, the UK’s chief scientific adviser, said other measures may be necessary – including school closures – at some point.
“Those things need to be done at the right time,” he said.
The UK government’s chief medical adviser, Prof Chris Whitty, said the chance of dying with the virus “for any individual person” was “very low”.
But he added that if one person in any household starts to display symptoms, everyone living there must stay at home for 14 days.
Mr Johnson said the 14-day stay at home advice “means that if possible you should not go out, even to buy food or essentials, other than for exercise and in that case at a safe distance from others”.
Prof Whitty said social restrictions would be “very difficult for people to maintain” but they would be “doing it to protect the NHS from being overwhelmed”.