The charity claims that only 4% of the products it found on promotion in a survey of five supermarkets were labelled in accordance with industry best practice.
Only 18% of products carried information about sensible drinking levels and 56% included unit information, Alcohol Concern said.
The charity said the findings were disappointing, as a voluntary labelling agreement has been in place since 1998 and the drinks industry pledged to make improvements to labelling in 2008.
Chief executive Don Shenker called on the government to introduce mandatory health labelling on drinks.
He added: “There is a huge disparity between the drinks industry’s enthusiasm to promote and advertise alcohol to the public and their willingness to give consumers the facts about what they are drinking.
“Supermarkets promote alcohol at irresponsibly low prices and do very little to ensure that consumers have sufficient information to make healthy choices about their consumption. Profit is clearly being put above public health and it is time for government to act.
“Supermarkets claim they act responsibly in addressing alcohol misuse and yet they consistently fail to live up to their corporate responsibility statements. They have a unique opportunity to only sell and promote products that are clearly labelled and we call on them to do so from now on.”
Alcohol Concern looked at 10 promoted products in branches of Sainsbury’s, Tesco, Asda, Morrisons and Waitrose. It tested the packaging and labels of these products against five criteria set out by the Department of Health as the ideal components of an alcohol label: unit information, sensible drinking guidelines, information about drinking while pregnant, the Drinkaware website address and the “know your limits” slogan.