The scheme, which would cost £5bn to implement nationally, had already launched in Manchester and London. Many retailers felt it would have made determining ages easier.
Association of Convenience Store chief executive James Lowman said: "We always knew the scheme was controversial, but members welcomed it."
Lobby group NO2ID said the decision was a victory for civil liberties, while Josie Appleton of anti-regulation group Manifesto Club went further, claiming that retailers asking for ID was more about the regulation of citizens than combating social issues.
Writing in The Guardian, she said: "Challenging this culture of ID checking is as crucial as taking on the ID card scheme itself. As free citizens we should not have to produce our papers at the local supermarket."
Lowman labelled Appleton's views as "ridiculous" and reminded retailers that from October, stores which sell cigarettes and alcohol will be required by law to run age-verification schemes. "Retailers who stand up to these problems and try to stop children buying these products should be applauded and supported, not vilified as part of some Orwellian plot," he said.
Lowman urged all retailers to continue to ask for ID for age-related products. "Don't wait for another scheme to be introduced because it won't happen," he said. "Keep asking for ID and implement a challenge policy to ensure that you don't fall foul of the law."