Lads' mags must be covered up in modesty bags or 4,000 Co-operative stores will refuse to stock them, the company has announced.
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 Sport newspaper has already agreed to deliver all editions to stores in bags from September 9, the Co-operative said.
Shelves of "lads' mags" on display in an Edinburgh newsagents
Sophie Bennett, a spokeswoman for Lose the Lads' Mags campaign group, said the issue was not nudity, but sexism, and called for the Co-operative to stop stocking the magazines altogether.
She said: "Thousands of people have called on retailers to stop selling lads' mags like Nuts and Zoo. The Co-operative's actions show our voices are being heard.
"Yet the Co-operative are attempting to sell their customers short. The so-called 'modesty bags' they are demanding from publishers are designed to allow the Co-operative to continue profiting from sexist, harmful lads' mags - but just a bit more discreetly.
"That's not what corporate social responsibility looks like."
Well done @CooperativeFood for their lads mag stance. Been annoyed/shamed by barely concealed nipples at eye level in shops for years
— Steph Edusei-Basra (@StephEBas) July 29, 2013
Lets face it, you don't see anything on the cover of a lads mag than is seen on beaches all over the world. #crazyworldwelivein
— Ian Hutchinson (@hutchi13) July 29, 2013
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.
Steve Murrells, retail chief executive for the Co-operative Group, said: "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."
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."
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