The Prime Minister said anyone who lives with someone who has a cough or a temperature should stay at home for 14 days.
He went on to set out the need for "drastic action" to tackle the "fast growth" of coronavirus.
The Prime Minister said that according to the Scientific Advisory Group for Emergencies (Sage) ‘it looks as though we are now approaching the fast growth part of the upward curve" in the number of cases’.
"Without drastic action cases could double every five or six days," he said.
Speed of virus
Mr Johnson said London appeared to be "a few weeks ahead" of other areas and urged people in the capital to pay special attention to the measures - including home working - suggested by the Government.
He add: "if you or anyone in your household" had one of the two symptoms - a high temperature or continuous cough - "you should stay at home for 14 days".
"That 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," he said.
In a dramatic escalation of the Government's response, Mr Johnson said that even those without symptoms needed to take extra action.
"Now is the time for everyone to stop non-essential contact with others and to stop all unnecessary travel," he said.
Mr Johnson said that from Tuesday the Government would no longer be supporting mass gatherings with emergency workers.
Mass gatherings are something "we are now moving emphatically away from", he said.
Avoid pubs, work from home
The Prime Minister said people should start working from home "where they possibly can".
"You should avoid pubs, clubs, theatres and other such social venues," he said.
Mr Johnson said by the weekend, groups particularly vulnerable to Covid-19 will be asked to stay at home for 12 weeks.
He said: "In a few days time, by this coming weekend it will be necessary to go further and to ensure that those with the most serious health conditions are largely shielded from social contact for around 12-weeks.
"Again, the reason for doing this in the next few days rather than earlier or later is that this is going to be very disruptive for people who have such conditions."
Asked whether pubs, restaurants and theatres were being ordered to close, the Prime Minister said: "What we are doing is giving very strong advice that public venues such as theatres should no longer be visited.
"The proprietors of those venues are taking the logical steps that you would imagine, you are seeing the change happen already.
"As for enforcement, we have the powers if necessary but I don't believe it will be necessary to use those powers."
The Government's chief scientific adviser Sir Patrick Vallance said the latest measures to combat the spread of Covid-19 would have a "big effect".
"This is not a series of small interventions. You would anticipate that this could have a dramatic effect to reduce the peak and to reduce death rates," he said.
"They are not easy but they are important and they will have the effect if we all do it.
"This is a matter for us to take accountability to make sure we help each other, protect ourselves and protect the NHS."