Morrisons, Sainsbury's, Asda, Tesco and Waitrose say they will deny entry to anyone not wearing a face covering unless they have a valid medical reason. Sainsbury's has also asked people to shop alone wherever possible.
Meanwhile Wolverhampton's Director of Public Health John Denley and Chief Supt Andy Beard of Wolverhampton Police have written to supermarkets and other key retailers asking them to review their Covid-19 risk assessments.
It follows a dramatic rise in infection rates locally and nationally, driven in part by a new, more contagious variant of Covid-19.
Retailers are asked to do a number of things, including reminding customers of the need to wear face coverings, ensuring staff and customers are able to follow social distancing measures by limiting the number of shoppers in store and managing queues, carrying out cleaning more often, encouraging customers to use hand sanitisers or handwashing facilities and asking shoppers to avoid handling products while browsing as much as possible.
John Denley, Wolverhampton's Director of Public Health, said: "We have started to receive more reports from shoppers about Covid-19 rule-breaking within stores being ignored, and being accepted. This is both concerning and alarming given that around one in 40 people in Wolverhampton currently have the virus.
"At this time, our city’s priorities must be to look after our most vulnerable residents, protect the NHS and save lives. We all have a collective responsibility to deliver this. So, we are writing to supermarkets and other major retailers in the city – who have done an incredible job continuing to serve customers throughout the pandemic – outlining the steps they need to take to keep their staff and customers safe.
"We welcome the news that big supermarkets are going to be much more rigorous in their enforcement of the wearing of face coverings indoors, and all shoppers now need to play their part by ensuring they are following the rules.”
Chief Supt Andy Beard said: "Over the coming days we will continue to work alongside the council as they undertake inspections to ensure stores are doing everything they can to keep their staff and customers safe.
“With our partners, we will continue to work with businesses to help them understand the regulations and, where we find significant issues of concern, will consider using enforcement powers."
Latest figures show there were 854.7 cases of Covid-19 per 100,000 people in Wolverhampton over the 7 days to 11 January. That means 2,248 people in the city tested positive for the virus in that 7 day period – though the true number of new cases will likely be considerably higher.
The latest information and guidance around coronavirus is available at GOV.UK and on the council’s own coronavirus pages. Further details of the lockdown restrictions currently in place, and the answers to frequently asked questions, are available at Covid Alert.