It comes just two days after senior Cabinet Office minister Michael Gove said he did not believe masks should be mandatory and that it was better to "trust people's common sense".
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The Government has been reluctant to enforce the wearing of face coverings, and its guidance states they do not protect the wearer but may protect others if people are infected but have not yet developed symptoms.
He told MPs that retailers should "call the police" if anyone refuses to wear a face covering from 24 July.
Face coverings are already compulsory on public transport in England.
However, Metropolitan Police Federation chairman Ken Marsh said the idea that police could enforce the new regulations was "absolutely absurd".
"I think that it is basic good manners, courtesy and consideration, to wear a face mask if you are, for example, in a shop".
In Scotland, which has its own powers over public health, it is already compulsory to wear face coverings inside shops.
However, many thousands of children likely to travel by public transport in September to get to and from school, there is likely to be more clarification on this policy the closer we get to the start of the new school year as transport and education bosses publish their plans.
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Dr Maria Van Kerkhove went on to say that a "comprehensive package of interventions is required to be able to stop transmission". They pointed to the risk of infection not only through large droplets but also smaller particles lingering in stagnant air.
Those who flout the law can be fined up to $180 by the police under public health laws.
The use of masks is said to help prevent the chance of spreading the virus to others - with the masks said to block droplets containing the virus from entering the air.
The Government has been encouraging people to wear face coverings in confined spaces such as shops since early May.
He also suggested evidence that face coverings increase people's confidence to shop.
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".
Wearing a face covering doesn't replace the need for frequent thorough hand washing and following social distancing guidelines, and it's still important to self-isolate if you have coronavirus symptoms. I think the delay up to the 24th is quite confusing as well'.
The confirmation follows Johnson's intervention over the issue on Monday, when he called on people to wear masks while the government considers enforcement measures.
"We'll be driving around and around London looking for people who aren't wearing masks".
The professional trade union of the retail trade welcomed the "clarity" of this obligation, after "contradictory messages" which made "really hard for people to understand what they had to do". Evidence shows that widespread wearing of face masks can reduce the spread of infection.