One of Britain's largest magazine retailers has threatened to withdraw so-called "lads' mags" from sale in its 4,000-plus stores unless publishers put them in sealed modesty bags to obscure the sexual images on the covers. The move by the Co-operative Group follows the introduction of opaque screens on its supermarket shelves this month– a preventative step until publishers provide their own modesty bags.

Publishers of titles such as Front, Loaded, Nuts and Zoo have been given until 9 September to deliver the magazines in pre-sealed bags designed to obscure the front cover, otherwise, the Co-op says, it will stop selling the magazines.The supermarket chain says that the move is in response to growing concern among its members, customers and colleagues about the exposure of children to the overt sexual images on such front covers which, despite the retailer's efforts, are still sometimes visible in-store.

Steve Murrells, chief executive of food and retail for the Co-operative Group, said: "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. While 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."

The Sport newspaper has already agreed to deliver all editions to Co-op stores in this way from September, following pressure from the retailer.

The Co-op's move comes two years after a recommendation by the government-appointed Bailey review that such magazines and newspapers should be displayed only the top shelf or have the images on the front covered by a "modesty sleeve". The National Federation of Retail Newsagents' code of practice says that adult material should be on the top shelf. It also recommends that men's lifestyle magazines should not be displayed next to children's titles or at a level at which they can be seen by children.The six-month review was launched amid concern about the commercialisation and sexualisation of children in Britain. The author of the report, Reg Bailey, chief executive of the Mothers' Union, said he hoped his review would help tear down the sexual "wallpaper" surrounding today's young people and give parents a stronger voice in regulation.

On behalf of the magazines' publishers, a spokesperson for the Professional Publishers Association (PPA), said they were acting responsibly and within government guidelines. "Men's lifestyle magazines are mainstream titles enjoyed by a readership of millions and feature content to reflect the diverse interests of the nation's young men. The average age of a reader of men's lifestyle magazines is 30, according to the National Readership Surveyand these titles are not created for, or marketed to, children. Publishers support the guidelines on the appropriate display of men's lifestyle magazines, which have been drawn up with the National Federation of Retail Newsagents and endorsed by the Home Office."

But Jo Swinson MP, minister for women and equalities and also minister for employment relations and consumer affairs, 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."

She said 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."

Sophie Bennet, spokeswoman for the Lose the Lad's Mags campaign by UK Feminista and Object said that the Co-op's move did not go far enough. "The more accurate term for these so-called "modesty bags" is "misogyny bags" because the issue for the thousands of people who have called on shops to lose the lads' mags is absolutely not about nudity. It's about sexism. And if a product is so degrading to women that it has to be covered up then the Co-operative should not be selling it.

"By stocking magazines like Nuts and Zoo, retailers like the Co-operative and Tesco are sending out the damaging message that it is normal and acceptable to treat women like dehumanised sex objects. Continuing to profit from sexist magazines would be at fundamental odds with the Co-operative's claim of being the 'UK's leading responsible retailer'."