The mayor has previously urged Londoners to wear face coverings and said he will “continue to try and lobby the government” on making them compulsory across the UK.
“We don’t want confusion,” Mr Khan told the London Assembly on Thursday. “When there is a crisis, what’s important is to have message clarity.
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“What I want is a consensus around this issue. I’ve been speaking to colleagues in Scotland, Wales and across the country, and I’ll continue to try and lobby the government on this one.
“We’ve been successful on other issues. I’m hoping to be successful here, but I leave the option available, which is to make it mandatory in London only. But I’m hoping we can persuade the government to do the right thing.”
Mr Khan said he wants to work with the government “to reach a sensible compromise”, as he noted that some train services in London are not under his control, but said that next week he would consider using his powers as mayor to make face masks compulsory.
Scientists, including those in the government’s advisory group, Sage, are divided over the efficacy of face masks and coverings in protecting against coronavirus, which significantly reduce the spread of “droplets” of infection.
However, others remain concerned that incorrect usage of masks could negate these benefits.
The government itself has given contradictory statements on their usefulness, finally recommending their usage in enclosed public spaces on 11 May, the day after Boris Johnson urged people to return to work.
The prime minister had previously said they would be “useful” once lockdown was eased to ”give people confidence they can go back to work”, two days after health secretary Matt Hancock denounced the Scottish government’s advice to wear masks as being based on “weak science”.
NHS bosses have warned that supplies must be prioritised for health care workers, with NHS Providers chief executive Chris Hopson cautioning in April that there must be “clear evidence” to justify their widespread usage.
It came as the British Medical Association said there was some emerging evidence that face coverings may help in controlling the spread of Covid-19, recommending all key workers, such as shopkeepers, carers and transport workers, be provided with masks.
On Wednesday, Mr Khan wrote to all major supermarkets, urging major retailers, corner shops and Tube station outlets to sell face masks.
“Whilst we at City Hall are encouraging the use of homemade face coverings, I recognise that there will be many Londoners who will need or want to purchase a ready-made product instead,” he wrote.
“I am therefore urging you to stock supplies of reusable, non-medical face coverings in all of your London stores, at a price point that makes them accessible to all Londoners.”
Speaking to BBC Radio 4’s Today programme on Thursday, Mr Khan said he remained “very cautious” about lifting more lockdown restrictions, fearing a second wave of infection.
Discussing declining transmission rates in the capital, he said: “What this good news – and it is good news – gives us is, a window of opportunity to begin the test, trace, isolate and support programme which we so desperately need.
“Let me tell you why: we know that test, trace, isolate works best when numbers are low and we’ve got a small window now to be testing everyone that has got symptoms, to be tracing everyone they have been in contact with over the last few days and then to make sure they are tested, isolated and supported.
“Because my fear is that this good news could lead to complacency, which could lead to a second wave that would overwhelm the NHS and be really bad for people’s lives, but also their livelihoods.”
Additional reporting by PA