The government's top medical adviser has drawn up plans for a minimum price for alcohol which would double the cost of some drinks in England.
Under the proposal from Sir Liam Donaldson, no drinks could be sold for less than 50 pence per unit of alcohol they contain.
It would mean most bottles of wine could not be sold for less than £4.50.
Cabinet minister Douglas Alexander said the government would consider what Sir Liam had to say in his report.
But Work and Pensions Secretary James Purnell said ministers had no intention of going ahead with something that would punish the responsible majority of drinkers.
The proposal is aimed at tackling alcohol misuse and is set out in Sir Liam's annual report on the nation's health.
A Department of Health spokeswoman said: "We have not ruled out taking action on very cheap alcohol - it's clearly linked to people drinking more and the subsequent harm to their health."
She said more work needed to be done to make sure action was "appropriate, fair and effective" but decisions would take the "wider economic impact during this difficult time" into account.
Shadow health secretary Andrew Lansley said it was important to deal with people's attitudes and not just the supply and price of alcohol.
The Liberal Democrats backed Sir Liam's stance and said putting an end to "pocket-money priced alcohol" would influence drinking behaviour.
Carys Davis of Alcohol Concern said that setting a minimum price for alcohol would help deter youngsters from binge drinking.
She said: "It tends to bring up the prices of the alcoholic drinks that are drunk by harmful and very young drinkers, whereas you'll find that moderate drinkers tend not to really see a negligible financial effect."
Dr Chris Record, a liver specialist at the Royal Victoria Infirmary in Newcastle, said there was a "very, very close link between price and consumption" and increasing the price of alcohol would "target those people that are drinking at harmful or hazardous levels".
A Tesco spokeswoman said: "If government comes forward with a package of proposals including minimum alcohol pricing, we would enter into discussions positively".
The Portman Group, set up by drinks manufacturers to promote sensible drinking, opposes the plan.
Portman chief executive David Poley said: "This would have a marginal effect on harmful drinkers but force hard-working families to pay more for a drink."
Earlier this month the Scottish government published plans for a minimum price per unit of alcohol, which is strongly opposed by retailers and the drinks industry. No price threshold was set.
Setting a minimum price could have a particular impact on "own brand" or "value pack" beers and ciders.
Sir Liam's report is due to be published on Monday. The proposals as they stand do not apply to Wales or Northern Ireland.
The BBC's health correspondent Adam Brimelow said Sir Liam's recommendation would not automatically become government policy.
But he said Sir Liam was influential and had advocated a ban on smoking in public places long before it became law.
The NHS bill for alcohol abuse is an estimated £2.7bn a year.
The most recent figures show hospital admissions linked to alcohol use have more than doubled in England since 1995.
Alcohol was the main or secondary cause of 207,800 NHS admissions in 2006/7, compared to 93,500 in 1995/96.
The figures include hospital admissions for a specific alcohol-related condition - such as liver disease, but also admissions where alcohol is a contributory factor but not the main cause - such as falls due to drunkenness.
Of hospital admissions in 2006/7 specifically due to an alcohol-related diagnosis, almost one in 10 were in under 18 year olds.
The number of alcohol-related deaths in England has doubled since the early 1990s to nearly 9,000 a year.