Masks must also be worn in shops in Scotland, and will be mandatory in shops in England from 24 July, with shoppers facing a £100 fine if they refuse to comply.
With the economy taking a battering, the government is desperate to get us back into shops and spending again.
During an interview with BBC Radio 4's Today program on Tuesday, Ken Marsh - who represents police officers in the United Kingdom capital - claimed it would be "nigh-on impossible" to enforce the new requirement on face masks, due to come into law in England on July 24.
"Shopkeepers need to step up to the plate and take some responsibility", said Mr Ken Marsh of the Metropolitan Police Federation, which represents rank-and-file officers.
But the new laws will therefore apply to older children, teenagers and young people either shopping by themselves or with family members who may need to get used to carrying coverings at all time.
In Scotland, which has its own powers over public health, it is already compulsory to wear face coverings inside shops.
The Opposition Labour Party, which has been in favour of stricter enforcement of face coverings as a measure to curb the transmission of coronavirus, had called for more clarity after some contrary messages on compulsory face coverings. Shops and business owners will be asked to help ensure customers follow the rules but only police can issue the penalty fine.
Coronavirus in Suffolk: Face coverings and masks mandatory in shops
The prime minister described face coverings as "extra insurance", while levels of Covid-19 continue to fall. Click the link in the orange box below for details.
Britain and France previously took a more relaxed attitude to face coverings than many other European nations, recommending masks but not requiring them.
Mr Hancock replied: "The balance in the need to restrict the spread of the virus, whilst also allowing the ancient liberties of a gentleman to go shopping, is a hard balance to strike and we have made the judgment that the best way to strike it is to allow a gentleman to go shopping, but require him to wear a face mask".
Mr Gething said: "There will be a range of people who won't be able and shouldn't wear a face covering".
It has been made clear that "face coverings are not the same as face masks" and that they "can be made from scarves, bandanas or other fabric items, as long as they cover the mouth and nose".
Mr Scott said: "I don't think it will deter shoppers, I think people are fairly compliant".
The city's director of public health, Sharon Stoltz, said: "I would ask residents not to wait until 24 July and start wearing face coverings now in all public spaces".
"If you are not wearing a mask and have the virus, you could spread it to so many people".
But Labour, the opposition party in the United Kingdom parliament, has accused the government of having "a lack of clarity" on the issue. If you're in the United Kingdom, the National Health Service can also provide useful information and support, while US users can contact the Center for Disease Control and Prevention.