UK shops are to be banned from selling wine, beer or spirits for less than the cost of duty and VAT.
The coalition government believes the move will stop alcohol being sold at a big loss to lure customers.
Police are worried the glut of bargain booze has fuelled the current binge-drinking culture in England.
The minimum pricing would work out at 38p for a can of weak lager and £10.71 for a litre bottle of vodka.
However, Prof Ian Gilmore, of the Royal College of Physicians, told the BBC that in practice the move was a “small step” with “no effect at all on the health of this nation”.
He said he guessed that less than 1 per cent of drinks were currently sold below duty plus VAT: “I’m afraid it is window dressing at the moment.”
The British Medical Association also said the proposals did not go far enough and would not make much difference.
And Don Shenker, chief executive of Alcohol Concern, said: “Duty is so low in the UK that it will still be possible to sell very cheap alcohol and be within the law.
“The government needs to look again at a minimum price per unit of alcohol. That is the only evidence-based approach that will end cheap discounts once and for all.”