The home secretary has left open the possibility of a minimum price on alcohol of more than 40p a unit, insisting that the government's plans to introduce legislation on the cost of drinks could help end the "drunken mayhem" in town centres and cut violent crime.

Speaking as David Cameron prepared to risk the wrath of the drinks industry and free-marketeers, Theresa May insisted that "all the evidence" showed the imposition of a minimum price on alcohol had an effect on the problems linked with drinking too much.

The government claims the 40p minimum could mean 50,000 fewer crimes a year and 9,000 fewer alcohol-related deaths over the next decade. The move is regarded as the biggest public health intervention since the Labour government's smoking ban.

"The evidence – the international evidence but also the historic evidence – is that if you need to deal with problems that are caused by excessive consumption of alcohol, what you have to address is the price of it," May told BBC Radio 4's Today programme.

Asked whether the government would stick with the figure of 40p as a minimum price per unit, May refused to be drawn on the possibility that it could eventually opt for a higher figure. The government would be consulting on the issue, she said, to "see what the appropriate level is. We will listen to the consultation and we will take a decision accordingly."

She added: "There are too many town centres around our country where sadly, particularly on a Friday or Saturday night, the scenes in them of drunken mayhem are ones which mean that an awful lot of people just don't go into those town centres, or if they do they don't enjoy it, because of what's happening around them, let alone the problems it causes for the police and of course the problems it causes for hospitals with the number of people turning up in accident and emergency units because of drunkenness."

The drinks industry has criticised the move, claiming that minimum pricing will be ineffective and unfair. Gavin Partington of the Wine and Spirit Trade Association told the BBC: "The international evidence is that problem drinkers are least likely to be deterred from drinking by price rises." He said the measure would punish the poorest people.

The British Retail Consortium labelled it "seriously misguided" and a "tax on responsible drinkers" that would not deter bingers.

The government says the cost of a 40p minimum would be £21-£23 a year for average drinkers. May said the move would primarily affect the "cheap end" of the market, which she characterised as consumers who were buying alcohol and "pre-loading"– drinking at home before going out.

Sir Ian Gilmore, the Royal College of Physicians' special adviser on alcohol, insisted a minimum price was "the fairest way" to tackle binge drinking. "Alcohol's never been cheaper in real terms, and we're now seeing supermarkets selling drink at pocket-money prices," he said. "The fairest way to tackle this is to put a minimum price floor because it won't affect the price of a pint of beer in a pub … but it will hit the very heavily discounted cheap cider."

The aim is to introduce legislation in the autumn after a summer consultation, with the minimum price coming into force in 2014.

Guardian analysis suggests the government's proposed minimum price would substantially curtail many of the high-profile drinks deals promoted by major supermarkets. Data provided by the research company Assosia, covering promotions between December and February this year, shows Tesco and Sainsbury's offered two-for-£20 deals on 20-pack crates of Strongbow cider – a sale of more than 93 units of alcohol, working out at just 21p per unit.