The Co-operative has given publishers of lads' magazines an ultimatum to cover them up in "modesty bags" or face having them removed from shelves across 4,000 stores.
Titles such as Front, Loaded, Nuts and Zoo - known for their pictures of scantily-clad models - have been given until September 9 to deliver the magazines in pre-sealed bags.
The retail group, which describes itself as one of the UK's largest magazine sellers, had already introduced opaque screens on shelves earlier this month to shield children from "lewd pictures" on front covers. It comes amid increasing debate about the effects of sexual images on children, with David Cameron setting out a raft of reforms this week which will introduce family-friendly filters that automatically block internet porn unless customers choose to opt out.
The Co-operative said the move was a response to concerns by its members, customers and colleagues, with Steve Murrells, retail chief executive for the Co-operative Group, saying: "As a community-based retailer we have listened to the concerns of our customers and members, many of whom say they object to their children being able to see overt sexual images in our stores.
"Whilst we have tried to mitigate the likelihood of young children seeing the images with a number of measures in-store, the most effective way of doing this is for these magazines to be put in individual, sealed modesty bags.
"As an interim measure, we have introduced our own opaque screens on shelf to reinforce our existing policy limiting the display of such material. The publishers of these magazines now have until September 9 to start providing their own modesty bags, after which any lads' magazine which does not have the relevant bag will not be supplied in our stores."
The Sport newspaper has already agreed to deliver all editions to stores in bags from September 9, the Co-operative said.
Jo Swinson, Minister for Women and Equalities, said: "Many parents aren't comfortable with the way that sexualised imagery has become like wallpaper - everywhere from the bus stop to the corner shop.
"Exposing children to lewd pictures that portray women as sex objects is not appropriate. That's why The Co-operative's decision to implement the Bailey review recommendation for publications with overtly sexual images on the cover to be displayed and sold in modesty bags is very welcome.
"Adults should be left to make their own decisions about what legal sexual images they look at, but the place for these is not next to the sweets at children's eye-level. I hope other retailers will follow the Co-operative's lead."