Economic secretary to the Treasury Chloe Smith told MPs the government believes minimum pricing “could be incompatible with article 34 of the treaty of the functioning of the European Union”, and also said imposing higher VAT on drinks sold in supermarkets would breach European law.

In a debate secured by Tory backbencher Dr Sarah Wollaston, a succession of MPs said the UK’s problem with alcohol stemmed largely from discounting in the off-trade.

Wollaston said: “There is a wealth of evidence to link alcohol price increases and reduced rates of homicide, rape, robbery, assault, motor vehicle theft and domestic violence.”

She added: “The widening gap between the price of on-licence and off-licence alcohol is becoming far more significant and is fuelling the rise in home drinking. Harms are not going down as we might expect as a result of the small fall in overall consumption, because of the low-price deals that are still very widely available in supermarkets, garages and convenience stores pretty much around the clock.”

During the debate, Asda was criticised for labelling a 68p four-pack of ale as “smart price”, and Tesco was condemned for marketing tactics that encouraged shoppers to buy from English stores when minimum pricing for alcohol is introduced in Scotland.

Smith said she shared concern about alcohol abuse and would consider evidence-based proposals to deal with it, in addition to measures already taken by the coalition.