Boris Johnson said the spread of coronavirus in London was “weeks ahead” of the rest of the country, urging people to stay at home and keep distance from friends and family.
On Friday the prime minister ordered the closure of all restaurants, pubs, bars and other social venues.
Next week, an emergency bill going through Parliament will give police special powers to enforce the law.
Speaking on the BBC’s Andrew Marr Show on Sunday, the mayor of London admitted that “life has changed”, urging Londoners to take the spread of the virus more seriously.
Now fully aware of the accelerated situation in London, Khan said: “I am really quite clear: people should not be leaving their homes unless they have to.
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“Sometimes there is a good reason to leave your home, such as to walk your dog or get some exercise, but what we really shouldn’t be doing is having social interaction.
“Be under no doubt – by mixing it leads to more people dying.”
He continued: “I am not someone who says these things lightly but unless people don’t stay at home, if they don’t stop using pubic transport unless it’s essential, unless people will stop interacting with people, more people will die.
“That’s why it’s really important that people start to recognise the scale of the challenge ahead of us.
“Please, please please – stop mixing. Stay at home.”
When asked if the police or army would intervene, the mayor said imminent enforcement legislation will be used if necessary.
He continued: “If people continue to act in a way that is leading to this disease spreading, then those sorts of things will be things that will have to be considered.”
The mayor also said that the provision of a limited skeleton public transport system should be avoided, emphasising the system remained open for “critical workers” only.
Marr asked Khan if he should suspend the London transport network entirely, in case NHS workers contract COVID-19 themselves and spread it on buses and tubes.
Khan said: “I’m really keen to make sure transport is available to critical workers, to get to and from work and home.
“We are trying to make sure there are enough tubes and buses so that they are not overcrowded.
“Nobody else should be using transport, nobody else should be leaving their home.”
Khan also reiterated his message on Twitter, posting on Sunday morning: “IMPORTANT: My message to Londoners: Do not leave home unless you have a very good reason.
“Do not go to work or use public transport, unless you do a critical job. Ignoring these instructions will cause more people to die.”
IMPORTANT: My message to Londoners:— Sadiq Khan (@SadiqKhan) March 22, 2020
➡️ Do not leave home unless you have a very good reason.
➡️ Do not go to work or use public transport, unless you do a critical job.
Ignoring these instructions will cause more people to die. #COVID19 #Marrpic.twitter.com/Xb8w1xmAbS
Also on Sunday, housing minister Robert Jenrick warned that asking people to stay at home to suppress the number of COVID-19 cases was not "a game" – and refused to rule out tougher action.
Speaking on Sky News’ Sophy Ridge on Sunday, he said: "We have now closed the pubs, the restaurants, the clubs, the indoor gyms and leisure activities, and we want people now to follow that advice and stay at home wherever possible.
"If people don't follow that advice, we'll clearly have to consider other options. But none of us want to go down that route."
However, according to a YouGov survey published on Saturday, nearly three-quarters of people say they have changed their behaviour following government guidance.
The survey, commissioned by Imperial College London’s Patient Experience Research Centre, said that almost half of those surveyed believe they will eventually contract the virus.