The mayor said that evidence from around the world was that face coverings help stop the spread of the virus.
According to him: "The latest scientific evidence shows that they can reduce the chances of an individual unknowingly infecting other people with COVID-19 and can therefore help to slow the spread of the virus."
"This is consistent with the advice from the World Health Organisation (WHO) and with actions in other cities and countries around the world, many of whom have made wearing a face covering, especially when it is not possible to socially distance, a requirement before lifting lockdown."
Mr Khan added: "I am therefore urgently seeking your support on making the wearing of face coverings obligatory when using all public transport.
"Here in London, that consistent approach to all public transport is important, given not all of it is under my control."
The mayor said such a move would "protect staff and passengers now" and would also be useful when the lockdown started to be eased - a time "when there will be a challenge to maintain social distancing on an increasingly busy transport network".
Public Health England has emphasised the importance of masks for doctors and nurses treating patients with the coronavirus, but it has not suggested widespread public usage.
In United States, New York has ordered residents to wear masks or substitute face coverings when in any public situation that may not allow them to be at least six feet away from others.
“In those circumstances where its not possible for us to keep our social distance, think of public transport usage, think of when you’re in a shop, we should be using non-medical facial coverings like bandandas, like scarves, like reusable masks,” Khan told the BBC.
The United Kingdom’s social distancing guidelines do not mention the wearing of face masks, but Khan said that should change.
Britain’s lockdown was extended by at least three weeks on Thursday as its death toll rose to 13,729, and the opposition Labour Party leader Keir Starmer has cautioned that the country risked becoming the worst hit in Europe.
The government's chief scientific adviser Sir Patrick Vallance said on Monday that the UK's position on masks was under review and would change if the scientific evidence warranted it.
Mr Shapps also told Sky News' Kay Burley@Breakfast: "It looks like the advantages might be marginal - there can even be times when it's disadvantageous if they're not used properly.
"We must be guided by the science in defeating this virus at every stage."
The WHO has said people should only wear masks if they display symptoms of COVID-19 or are taking care of someone who does. But it has also said that a mask on its own is not enough to protect people from the virus, emphasising the importance of other preventative measures like hand washing as well.
While there is no conclusive evidence to say that masks can stop people from contracting COVID-19, it is accepted that they can block transmission to others.
In April, a study in Nature Medicine suggested surgical masks could help prevent infected people from making others sick with seasonal viruses, including coronaviruses.
(Sky News/ Reuters/ AFP)
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