The number of cases in London is now above 1,000 per 100,000 people, he said, with a 27 per cent increase in hospital patients between December 30 and January 6.
The 7,034 people currently in hospital with Covid-19 represents a 35 per cent increase compared to the peak of the pandemic in April.
Mr Khan said that over the last three days alone the NHS has announced 477 deaths in London hospitals following a positive test for Covid-19.
In a letter to Boris Johnson he has demanded churches and other places of worship be closed and for face masks to be worn routinely outside of the home, including in supermarket queues and other places outside that may be crowded.
In a statement Mr Khan said: ‘The number of cases in London has increased rapidly with more than a third more patients being treated in our hospitals now compared to the peak of the pandemic last April.
‘Our heroic doctors, nurses and NHS staff are doing an amazing job, but with cases rising so rapidly, our hospitals are at risk of being overwhelmed. The stark reality is that we will run out of beds for patients in the next couple of weeks unless the spread of the virus slows down drastically.
He said that over the last three days alone the NHS has announced 477 deaths in London hospitals following a positive test for Covid-19.
The Office for National Statistics found in its mass testing programme that almost two thirds (61%) of the positive tests it found in England appeared to be linked to the new variant of the virus. The figure was higher for some regions – particularly in London and the South – but lower in others
‘We are declaring a major incident because the threat this virus poses to our city is at crisis point. If we do not take immediate action now, our NHS could be overwhelmed and more people will die.
‘Londoners continue to make huge sacrifices and I am today imploring them to please stay at home unless it is absolutely necessary for you to leave. Stay at home to protect yourself, your family, friends and other Londoners and to protect our NHS.’
A major incident has already been declared in neighbouring Surrey and Sussex.
A major incident is defined as being ‘beyond the scope of business-as-usual operations, and is likely to involve serious harm, damage, disruption or risk to human life or welfare, essential services, the environment or national security’.
In addition, ‘the severity of the consequences associated with a major incident are likely to constrain or complicate the ability of responders to resource and manage the incident.’
It came as a new mass test revealed the highly infectious new variant of coronavirus that emerged in Kent now accounts for 61 per cent of all new Covid cases in England and 70,000 people are getting infected every day.
The team behind the ZOE Covid Symptom Study app, carried out with King’s College London, say the number of people reporting symptoms each day is up 27 per cent in a week from 55,226 to 69,958.
And separate research by the Office for National Statistics found that, of the estimated 1.1million people currently infected with the coronavirus, almost two thirds have the fast-spreading variant of the virus.
The variant has become dominant in some regions, found in 81 per cent of cases in London, but is still linked to fewer than half of infections in the North of England, the Midlands and Scotland, Wales and Northern Ireland.
Georgia Gould, chairwoman of London Councils, said: ‘Cases are rising at a dangerous rate in London, putting extreme pressure on the NHS.
‘One in 30 Londoners now has Covid. This is why public services across London are urging all Londoners to please stay at home except for absolutely essential shopping and exercise.
‘We know how tough this is for Londoners. Councils are here to support anyone struggling to access food or medicine.
‘Today, the thoughts of London leaders are with the thousands of Londoners in hospital battling Covid and the amazing carers fighting to save lives. We owe it to them to do all we can to keep ourselves and our loved ones safe.
‘This is a dark and difficult time for our city but there is light at end of the tunnel with the vaccine rollout. We are asking Londoners to come together one last time to stop the spread – lives really do depend on it.’