Bosses of Morrisons have announced that shoppers who refuse to wear a face mask without a medical exemption will be told to leave stores from today (January 11).
Those who flout the rules will be refused entry unless they are medically exempt, according to the supermarket's chief executive, David Potts.
He urged customers to "be kind", saying members of the public and staff at the supermarket should not be put at risk, as the coronavirus pandemic continues in the UK.
Potts said in a statement: "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."
The move comes after union Usdaw - Union of Shop, Distributive and Allied Workers - revealed it has been "inundated" with complaints from members who say they are "deeply concerned" for their safety as shoppers flout in-store coronavirus measures.
Usdaw has now supermarkets and food retailers to revert to "stringent" restrictions. It also said that staff - who are classed as key workers - must be "valued, respected and protected".
Other supermarkets, such as Tesco and Sainsbury's, said safety remains their "highest priority" and that customers were given regular reminders to follow the rules.
The new Morrison's rule comes as vaccines minister Nadhim Zahawi said he was concerned that members of the public were not following measures put in place by supermarkets, amid suggestions the restrictions may need to be toughened.
He said: "I am worried about supermarkets and people actually wearing masks and following the one-way system and making sure when it's at capacity they wait outside the supermarket.
Usdaw general secretary Paddy Lillis added: "Retail staff are working with the public every day and not only suffer increased abuse, but are deeply worried about catching Covid-19.
"Where safety measures are agreed, retailers need to make sure that they are being followed consistently, in every store.
"We are also very concerned by reports that too many customers are not following necessary safety measures like social distancing, wearing a face covering and only shopping for essential items.
"It is going to take some time to roll out the vaccine and we cannot afford to be complacent in the meantime, particularly with a new strain sweeping the nation.
"Many retail workers are at a greater risk of catching the virus and bringing it home to their families.
"Supermarket workers and delivery drivers have worked throughout the pandemic to keep the country supplied with essentials.
"These key workers must be valued, respected and protected."
A spokeswoman for Sainsbury's told The Mirror: "Safety remains our highest priority.
"We continue to have a range of measures in place to keep customers and colleagues safe in our stores.
"We have greeters outside our supermarkets and busy convenience stores to limit the number of customers coming into stores and continue to remind customers to wear face coverings and shop alone if they are able to.
"We also have posters and regular Tannoy announcements."
A Tesco spokesperson said it is still enforcing social distancing practices in store, however is not looking yet at reintroducing measures such as one-way aisles.
The store said on Twitter: "The safety of our customers and colleagues is our top priority and we already have extensive social distancing measures in our stores to ensure everyone can shop safely with us.
"We are asking all our customers to wear a face covering when visiting our stores and have prominent signs in place to inform customers of the rules."