All supermarkets are being urged to ensure customers are wearing face coverings while inside, after Sainsbury's and Morrisons announced security guards would be enforcing the rules.
Police Minister Kit Malthouse told ITV News that supermarkets "should be making sure that the customers who are coming in are observing social distancing and are wearing masks".
He said police would be on hand to assist with obstructive customers, pointing out that "700-odd" fines had already been issued by officers "in that kind of environment".
Face coverings have been mandatory in shops since July, but rising coronavirus cases across the country have prompted the government to reiterate their importance.
Kit Malthouse: 'Supermarkets should ensure customers wear face coverings...'
It comes after complaints that Covid-safety standards had slipped during England's third national lockdown, compared to the first, with widespread reports of people flouting the rules by shopping without face coverings and socialising in parks.
Sainsbury's followed Morrisons in announcing that customers would not be allowed in their stores without a face covering, unless they are medically exempt.
Morrisons Chief executive David Potts said: “Those who are offered a face covering and decline to wear one won’t be allowed to shop at Morrisons unless they are medically exempt.
"Our store colleagues are working hard to feed you and your family, please be kind.”
In an email to customers, Sainsbury's said: "When shopping in our stores you must wear a face mask or visor unless you have a medical exemption.
It added: "Security guards support our colleagues at the front of the store and will challenge customers who are not wearing masks or who are shopping in groups."
Tesco joined its rivals by making a similar announcement. A spokesperson said: "To protect our customers and colleagues, we won't let anyone into our stores who is not wearing a face covering, unless they are exempt in line with Government guidance.
"We are also asking our customers to shop alone, unless they're a carer or with children.
"To support our colleagues, we will have additional security in stores to help manage this. "
Mr Malthouse said police have been told to "think about moving to enforcement much more quickly", as he reminded supermarkets that officers will be working with them to make sure the rules are followed.
Metropolitan Police Commissioner Dame Cressida Dick has warned coronavirus rule-breakers they are “increasingly likely” to face fines as forces move “more quickly” to enforce lockdown restrictions.
Writing in The Times, she said: “It is preposterous to me that anyone could be unaware of our duty to do all we can to stop the spread of the virus.
“We have been clear that those who breach Covid-19 legislation are increasingly likely to face fines.”
She said officers in London had issued more than 300 notices in the space of 24 hours for "flagrant" violations of the regulations.
"That is quite a lot. I think it will have an impact and it will encourage more people to recognise that we are in a health crisis," she told BBC Radio 4's Today programme.
Mr Malthouse, who told ITV News more than 30,000 fines had already been handed out to rule-breakers, said enforcement of the is not designed to scare people but to encourage compliance.
He said: "It is very important that we stick to the rules now and make sure that we avoid having to take further steps."
"All of us want to make sure that this is the last lockdown that we have," he added.