
Any new bylaws would have to be approved by the home secretary The prime minister has voiced support for councils wanting to stop the sale of cheap alcohol.
David Cameron said plans in Greater Manchester to introduce a minimum price of 50p per unit would be looked at "very sympathetically".
Ten councils in the area want to pass bylaws to address public disorder and health issues caused by binge-drinking.
But he said while he supported local decisions, he did not want to introduce a national minimum price.
In an interview with the Manchester Evening News, Mr Cameron said: "I think the idea of the councils coming together on this is a good one and we will certainly look at it very sympathetically...
"Where there can be local decisions we are very happy for that to happen.
"It may be that we need to do something to help deliver the localist answer."
'Deep discounting'
He added: "I think if what you're trying to do is stop supermarkets from selling 20 tins of Stella for a fiver that's what we've got to go after.
"Where I want to try and help is ending the deep discounting on alcohol. People going and 'pre-loading', having bought from a supermarket where they were attracted by a price designed to bring them into the store."
Mr Cameron said a local bylaw could be challenged under competition rules, as it would mean alcohol in Greater Manchester being priced higher than neighbouring areas.
Any bylaws imposed by the authorities in Greater Manchester would have to be passed by the home secretary.
The House of Commons Health Select Committee and the National Institute for Health and Clinical Excellence have voiced strong support for minimum pricing.
But Health Secretary Andrew Lansley has expressed doubts on the grounds that it punishes low-income families.
The Department of Health said the government was committed to taking tough action over problem drinking but supply and price were far from the only factors driving alcohol misuse.
"Demand and attitudes are crucial. We need to understand much better the psychology behind why different groups of people drink alcohol in excess. No legislation or initiative will work unless we have a better understanding of what drives people's decisions," a spokesman said.
"We will work across government, society, communities and families to challenge negative social norms and promote the positives."
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BBC News - David Cameron backs local minimum alcohol pricing
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