Sadiq Khan is urging the Government to change its advice to the public on wearing face masks to combat the spread of Covid-19.
The London Mayor told BBC Breakfast on Friday that wearing non-medical facial masks, such as a bandana, scarf or reusable mask, would add “another layer of protection” to the public.
Current UK guidance has emphasised the importance of masks for doctors and nurses but does not suggest widespread usage.
Mr Khan, who wrote to Mr Shapps about the issue, said he is lobbying for masks to be worn in circumstances where people cannot keep two metres apart, such as on public transport or while shopping.
“Wearing a non-medical facial covering makes it less likely you may inadvertently give somebody else Covid-19,” he told BBC Breakfast.
“I want a consistent approach across the country, we don’t want mixed messaging.
“So I’m lobbying the Government’s experts and the Government, (and) want them to change their advice and change their guidance so we can have this additional layer of protection.”
Mr Khan added that everyone may need to wear a facial covering once the current lockdown measures begin to ease.
“What I’m lobbying for is, at the moment, when you can’t keep your distance, wear a non-medical facial covering,” he told the programme.
“But when it comes to exiting lockdown, we may need to have all of us wearing it as well.”
But Mr Shapps said the Government needs to consider all of the evidence on wearing face masks before issuing any new guidance.
Speaking to LBC on Friday, he said: “So it is not the right moment to instruct people, as I saw the London Mayor do this morning, to wear them if we are not certain yet that they are going to be advantageous.
“In fact, he wrote to me about this and said in his letter he recognises that it could be counter-productive, so I don’t think we should be in that space right at this moment.”
At Thursday’s press briefing, England’s chief medical officer Professor Chris Whitty said the Government is continuing to keep advice on wearing masks under review.
He said it would be a “very bad thing” if demand from the public for masks led to shortages for healthcare staff.
However, Prof Whitty said the Government’s Scientific Advisory Group for Emergencies (Sage) is considering whether there are circumstances in which if may be beneficial for the public to wear them.
He told the briefing: “The evidence is weak, but the evidence of a small effect is there under certain circumstances.
“What we are really trying to do is to work out under what circumstances, if any, should we extend the advice and under what circumstances should we not change that advice.”