The Co-operative chain has said it will stop selling "lads mag" Nuts magazine from next month after the title rejected its ultimatum to use "modesty bags" or be removed from shelves.
The magazine's publisher IPC Inspire has said that it will not use the bags and warned the issue was moving towards censorship. It described the ultimatum as "an unreasonable attempt to prevent shoppers from freely browsing a legal magazine that is already displayed according to Home Office guidelines".
The Co-operative, which calls itself one of the UK's largest magazine sellers, introduced opaque screens on shelves last 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 recently setting out proposals to block internet porn unless users specifically opt in.
Following the Co-operative's announcement, Tesco said it would sell lads' magazines only to over-18s. The supermarket said it had struck a "modesty deal" regarding the front covers of the magazines, and Bizarre would be supplied in a bag.
The Co-operative said: "Our position has not changed. If Nuts and Zoo, or any of the other publications, Loaded and Front, do not put their titles into modesty bags by the date we've given of September 9, we will no longer sell the magazines."
IPC Inspire managing director Paul Williams said: "The Co-operative's knee-jerk attempt to restrict access to a product that consumers have enjoyed for nearly a decade is wrong.
"Nuts takes its obligation to craft products that are right for consumers and retailers alike very seriously and for a number of weeks now we have had new covers in place, which have a more conservative tone. We are delighted with our readers' response to the new covers and last week's issue was our biggest-selling since February.
"As has been widely reported in the media in recent weeks, this is no longer a question of whether or not you like men's magazines, it is a question of how far you can restrict the public's ability to consume free and legal media before it becomes censorship."
Kate Jones, the Co-operative's head of product development, admitted that the store would lose money over the move.
Speaking on ITV's Daybreak, she said: "We will be losing money but we are responding to our customers' concerns.
"These are the publications that our customers are telling us they're concerned about. We do everything we can to ensure they are out of sight of children shopping in our shops.
"But sometimes during the trading day displays get disrupted. We think a modesty cover would be a fail-safe solution."