The mayor of London wants the government to change the guidelines about face masks, saying it should be compulsory to wear one while travelling in London.
Sadiq Khan isn't the only one. Dr David Nabarro, a senior British scientist with the World Health Organisation (WHO), recently said people would have to get accustomed to the "new reality" of wearing facial coverings in public.
As they gradually lift their lockdowns, governments across Europe are embracing this advice.
In Austria, anyone going into a store is obliged to wear a mask. German Chancellor Angela Merkel said this week that masks should be worn on public transport and in shops, once her country's lockdown is lifted.
Yet although chief scientific adviser Sir Patrick Vallance admitted the question was under review, UK authorities do not currently advise wearing a face mask in public.
What can the science tell us about this debate?
Before answering that question, it is necessary to make one distinction: between respirators, surgical masks and cloth face coverings.
This distinction may not be as important as it first seems, as the Centre for Evidence-Based Medicine suggests that "standard surgical masks are as effective as respirator masks for preventing infection of healthcare workers in outbreaks of viral respiratory illnesses such as influenza".
But the WHO currently says that any medical masks should be reserved for healthcare workers - and at a moment when personal protective equipment is in desperately short supply, no-one wants to deny them or other key workers the gear they need to do their jobs safely.
"It is extremely important that the supplies that are available are prioritised for healthcare workers and for other frontline essential workers such as supermarket checkout staff and public transport operators who are having multiple physical interactions with the public each day," says Dr Jennifer Cole, biological anthropologist at Royal Holloway, University of London.
That's why Mr Khan and others are calling for face coverings rather than masks.
Is there a benefit to wearing something wrapped round the bottom of your face, even if it's just an old t-shirt?
Until recently, scientists generally agreed that there wasn't, but the studies that formed the basis for this conclusion looked at influenza, rather than COVID-19.
Lately, there's been a change in the way scientists approach the question.
A new consensus is forming, which says that although a mask or covering might not protect an individual from an infectious droplet borne disease, it can help protect everyone else if that individual is sick.
This is especially relevant for coronavirus, because people are most infectious in the initial period after first being infected, when it is common to have few or no symptoms.
As emerging evidence suggests that even a piece of cloth can stop the droplets through which coronavirus is transmitted, this could be very helpful in stopping the spread of the disease without necessitating a lockdown.
This suggests that we should all be wearing masks when we go out, but, as ever, there is disagreement on the matter, because of the one factor that is unknowable: us.
The way we respond to face masks is crucial in determining their effectiveness. Some studies argue that wearing facemasks will encourage social distancing. Others claim it will undermine it by encouraging a false sense of security.
But given even a small chance that it might help us like without a lockdown, many researchers believe it's worth finding out.
As one recent study concluded: "If you have COVID-19 and cough on someone from 8 inches away, wearing a cotton mask will reduce the amount of virus you transmit to that person by 36 times, and is even more effective than a surgical mask.
"Oddly, the researchers who discovered this fact considered a 36-fold reduction to be 'ineffective'. We disagree.
"It means you'll transmit only 1/36th the amount of virus you would otherwise have done, decreasing the viral load, which is likely to lead to a lower probability of infection, and fewer symptoms if infected."
In other words: the science hasn't changed very much, but our perception of it has. We may soon get to discover whether people can maintain the kind of discipline necessary to make masks effective.