An end to bulk-buy discounts could also be on the cards as the Home Office launches a public consultation on the minimum price, thought to range from 40p to 50p per unit of alcohol.
At a unit price of 50p, the cheapest bottle of wine would rise in cost from around £3 to just under £5.
But Emily Robinson, of Alcohol Concern, said the "pocket-money prices" charged for booze have a long-term cost for the nation's health.
"Young people say it is cheaper to get drunk than go to the cinema," she said.
"So this is a measure that will target that group of people. It won't affect moderate drinkers much at all.
"And this is already costing us money. As taxpayers we are paying for the high costs in terms of policing, admissions to A&E and councils that have to clear up the mess."
Researchers at the University of Sheffield have studied the effect of setting a minimum price.
Charging at least 50p a unit would reduce the number of crimes by 42,500 in the first year.
After 10 years the policy would have prevented 15,000 deaths and 481,000 hospital admissions.
And it would save £9.7bn in its first decade, the research shows.
But the Wine and Spirit Trade Association said there was no "real world" evidence that minimum pricing would work.
Spokesman Miles Beale said the measure was unfair.
"Minimum pricing is not targeted at all," he said. "The vast majority of us are responsible drinkers but it will apply to us nonetheless.
"If a minimum price of 50p was introduced then 74% of products on supermarket shelves would go up in price."