Ministers have unveiled plans for a minimum price for alcohol in England and Wales.
They say banning shops and bars from selling drinks for less than the tax paid on them will send a "clear signal" they are serious about cheap alcohol.
It works out at 38p for a can of weak lager and £10.71 for a litre of vodka.
Health campaigners say that is too low to have an impact but the drinks industry described the proposals as a "pragmatic solution".
In their coalition agreement, the Conservatives and Lib Dems pledged: "We will ban the sale of alcohol below cost price."
Under government proposals the ban is on sales of alcohol below the rate of duty plus VAT, rather than including the cost of producing the drinks.
Last year, the Scottish Parliament rejected plans for a minimum price per unit of alcohol of 45p, after opposition MSPs said the move would penalise responsible drinkers and could be illegal under European competition law.
Announcing the plans for England and Wales, Home Office Minister James Brokenshire said it acknowledged "concern over how cheaply some alcoholic drinks are being sold" and the link between alcohol and disorder.
"Banning the sale of alcohol below the rate of duty plus VAT is the best starting point for tackling the availability of cheap alcohol and will send a clear signal to retailers and the public that government takes this issue seriously."
He said it would effectively set a minimum price and stop "the worst instances of deep discounting", would be a limited burden on business and would not cost must to implement.'Extremely small step'
But Professor Ian Gilmore, of the Royal College of Physicians, told BBC Radio 4's Today programme: "It's a step in the right direction but I have to say, it's an extremely small step. It will have no impact whatsoever on the vast majority of cheap drinks sold in supermarkets."
Researchers at Sheffield University estimated last year that raising the price of alcohol to a minimum of 50p per unit would mean that after a decade there would be almost 3,000 fewer deaths every year and 41,000 fewer cases of chronic illness.
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Prof Gilmore said a tiny amount of drinks were currently sold below duty plus VAT but said if the argument was being accepted that cheap drinks were fuelling alcohol problems the minimum might be "eased up in the right direction".
He said, in practice, the proposals would have "no effect at all on the health of this nation" and argued a minimum unit price would impact on heavy discounting in supermarkets.
The 50p-per-unit minimum was backed by health campaigners but the Home Office proposal is for a lower minimum price of about 21p per unit of beer and 28p per unit of spirits.
It means the lowest possible price of a can of lager would range from 38p to 78p depending on its strength, but most alcoholic drinks would be unaffected because they are priced above the level ministers are proposing.Moderate drinkers
A Home Office spokeswoman said it was a "sensible starting point" which could be introduced quickly and followed measures already announced to raise the tax on super-strength beers and lagers.
Gavin Partingdon, of the Wine and Spirit Trade Association, told the programme the proposals were a "pragmatic solution" which addressed some of the concerns about heavily discounted alcohol without affecting moderate drinkers.
He said they would stop retailers selling below cost price, although he accepted the amount of alcohol sold at below the level of duty and VAT was "fairly minimal".
Arora Avtar, shop owner, west London
"What lager is 38p? A bottle of vodka is £10 from the cash and carry anyway.
"I have to allow for my 10 to 15% margin so how can we charge less?
"The lowest price I can charge for lager is 89p for a can."
Sujaja Shah, of family-run AB wines, west London
"We can't loss lead - we'd go out of business. [Supermarkets] can buy in bulk.
"If the government wants to make an impact on drinking perhaps it should remove licences from supermarkets."
He said the 50p per unit minimum backed by campaigners went "way beyond what really the ordinary public want to pay".
"Professor Gilmore is suggesting that a policy which self evidently targets everybody can equally target those who have the most serious problem and yet any of us know... those who have the most problem with alcohol are least likely to be deterred by price increases."
The British Medical Association said the proposals did not go far enough and would not make much difference and Don Shenker, chief executive of Alcohol Concern, urged ministers to look again at a minimum price per unit of alcohol: "Duty is so low in the UK that it will still be possible to sell very cheap alcohol and be within the law."
Drinks giant Diageo said the proposal was "the least distorting option".
A spokeswoman for the firm said: "We believe the government should concentrate on raising awareness of the dangers of alcohol misuse for adults, providing effective education on alcohol for under-18s and enforcing existing legislation on licensing and under-age sales."
The coalition pledge was aimed at supermarkets who use alcohol as a "loss leader" to attract customers and make money from other items in the shopping basket.
But the proposed ban was left out of the Police Reform and Social Responsibility Bill in November, which included a major shake-up of the licensing laws.
Last month Tory MP Andrew Griffiths, secretary of the all-party parliamentary group for the Misuse of Drugs and Alcohol, warned that European competition law "prevents us from clearly targeting" what below-cost pricing meant.