Senior officers are concerned over the prospect of heated confrontations of the kind filmed in the US, where shoppers challenge people apparently refusing to cover their faces.
The Police Federation of England and Wales, which represents rank-and-file officers, said it would be “impossible” for them to enforce the law in every shop.
Chair John Apter said: “If you’re out shopping today and you see somebody not wearing a face covering it may be because they have a hidden disability.
“Don’t jump to conclusions, don’t have a go at them. This is new for us all, it’s about keeping each other safe. Please be nice.”
The new health protection regulations contain a lengthy list of exemptions, including people who cannot wear a mask “without severe distress”, or because of physical or mental illnesses and disabilities.
Several police and crime commissioners have anticipated confrontations, saying officers will not be sent to enforce the law unless there is “disorder or violence”.
Britain’s most senior police officer, Dame Cressida Dick, has said she hoped shoppers who refuse to wear masks will be “shamed” into compliance.
Privacy charity Big Brother Watch accused her of encouraging “bullying behaviour”, adding: “This is a public health situation, not a witch hunt.”
Official guidance issued to police officers in England on Thursday said that shops and other affected businesses should ensure masks are worn and can refuse entry if needed.
“Police officers’ attendance should only be required as a last resort,” the document says.
But several chains, including Sainsbury’s, Asda and Costa Coffee, have said they will not be challenging customers.
“We won’t be challenging customers without a mask when they enter or when they are in-store since they may have a reason not to wear a mask,” a spokesperson for Sainsbury’s said.
Asda said it would strongly encourage its customers to wear face coverings but warned: “It is the responsibility of the relevant authorities to police and enforce the new rules.”
But Mr Apter said it would be “impossible” for police officers to monitor all shops and businesses, as crime levels rise following the relaxation of lockdown restrictions.
He told Sky News people will be disappointed if “they think they are going to see police officers outside every store”.
“It is going to be impossible – we simply can’t do it,” he added.
“Policing has been stretched like never before. There are not enough of us to make this work.”
Anyone not wearing a face covering can be refused entry by an officer, be instructed to put one on or forced to leave the premises.
Adults who do not comply may be fined £100, reduced to £50 if paid within 14 days, but police guidance says enforcement should be a “last resort”.
A College of Policing document published on Thursday evening said police should check if people know the rules and help people find a face covering if they do not have one.
“For compliant individuals, no further action will need to be taken,” it says. “A constable may use reasonable force, if necessary, to remove someone, where they fail to comply with a direction to leave.
“As a last resort, officers may issue a fixed penalty notice for breach of the regulations or arrest where necessary. You may only exercise any of the powers if you consider they are necessary and proportionate.”
Police were told to be “professionally curious” about exemptions, and that they do not have to “assess the quality or suitability of the face covering so long as it meets the requirement of covering the person’s nose and mouth”.
The law, which was published on Thursday afternoon, states that “no person may, without reasonable excuse, enter or remain within a relevant place without wearing a face covering”.
A “relevant place” includes shops, banks and post offices, but not pubs, restaurants, cinemas, gyms and other leisure facilities.
It does not apply to “an area within or adjacent to a shop where seating or tables are made available by that business for the consumption of food and drink” by customers.
Children under the age of 11, staff, employees and people “providing services” for the business are not legally required to wear masks.
Retail bodies have voiced anger at the government over confusion, mixed messages and delays between the announcement of the change and the law coming into force.
Scotland made face coverings mandatory in shops from 10 July. People are not currently required to wear them in Wales or Northern Ireland but both nations are considering plans to make face masks mandatory in shops.
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