LADS' mags have been told to 'cover up or else' by The Co-operative.
It says photographs of scantily clad woman on the covers of Front, Loaded, Nuts and Zoo are "overtly sexual" and harmful to children.
The supermarket chain has given publishers of the four titles until September 9 to put them in modesty bags – or they will pull them from their shelves altogether.
The company has 4,000 stores, including at least 10 in Gloucester.
Its shops have already introduced opaque screens on shelves to shield the magazines from sight.
Longlevens dad-of-three Dave Jasper, 45, said: "It's a good idea as it prevents young people being exposed to that sort of thing.
"You don't want children to become accustomed to these images which I totally agree are overtly sexual."
Gloucester mum-of-four Patricia Blake, 38, said: "I don't have a problem with the magazines.
"You can see women in two-pieces at the beach and I don't think it's harmful for children."
Longlevens hairdresser Lisa Gregory, 45, disagreed and said her two children had said they do not like seeing the images.
The mum-of-two said: "If you choose to look at it then fine but children don't have a choice in a shop if it is right there in their face."
Account manager Mike Philpot, 19, from Longlevens, said: "If people don't want to look at them they don't have to.
"The images can be sexual but you see that kind of thing on the telly and in newspapers."
The Sport newspaper has already agreed to put a modesty bag on all editions sent to Co-operative stores from September 9, following pressure from the retailer.
Chief executive of retail for The Co-operative Group, Steve Murrells 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."
The Co-operative's decision comes after the Bailey review recommended publications with overtly sexual images on the cover be displayed in modesty bags.
Minister for Women and Equalities Jo Swinson MP said: "Exposing children to lewd pictures that portray women as sex objects is not appropriate. 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."