The Mayor of London said he first wrote to Boris Johnson three months ago to press the issue.
He told Sky News: “The evidence from around the world…was that this small thing with other measures can make a big difference.
“Of course I welcome this U-turn. What I don’t understand though is why wait two weeks? Why not do it from today?”
Last night it was announced that wearing a face covering in shops and supermarkets will be made mandatory in England in a bid to stop the spread of coronavirus.
Health Secretary Matt Hancock will say today that anyone who fails to comply with the order, which comes into force on July 24, could face a fine of up to £100.
Mr Khan said the Government had been “playing catch-up” throughout the pandemic and that the UK had been an “outlier”.
The Mayor said he had been asking the Government for more emergency Cobra meetings but that his requests had been refused.
He went on to accuse the Government of “group think” by not allowing themselves to be challenged which he said had led to “bad decisions”.
The Mayor went on to warn of a second wave in London, adding: "We’ve got to plan and prepare for that. There is a possibility of a second wave.
"All viruses in history have had second waves. The key thing is to avoid a convergence of a second wave of Covid-19 and the winter pressures there are on the NHS.
“There are practical things we can do to properly plan and prepare. The face covering decision is a first good step. We’ve got to make sure test, trace and isolate is fully operational.”
He also said the Government needs to make sure everyone in care homes and hospitals has the right personal protective equipment now rather than buy later in the year and people aged 50 or over getting a flu jab.
Meanwhile, Environment Secretary George Eustice defended the delay to ordering the mandatory use of face coverings.
He said: "The evidence, the understanding, has been evolving. So the World Health Organisation changed their guidance back in June and following that the Government changed its guidance and we recommended that people wear face coverings in enclosed spaces when they're out and about.
"We then sharpened that and made it compulsory for public transport in the middle of June and what we've really got here is, as we loosen the lockdown and allow more venues to open, we need to consider the mix of measures we have in place to limit the transmission and control the virus."
On BBC Breakfast he suggested that face coverings would not be compulsory for shop staff.
He added: "We want to give people time to plan and prepare and for retailers to maybe put in place measures to encourage people to do this or potentially even to have some masks themselves if people haven't got one."
Asked if the rules will apply to supermarket staff, he said: "They're not being covered by this but I think if you go into most shops you will see that staff for a longer time now have either been wearing face shields or face masks.
"It won't be a compulsory requirement because it won't always be right for every setting in a retail environment, particularly those working behind the tills and so on."