Speaking to the House of Commons science and technology commitee, which is looking into the evidence base for current alcohol guidelines, she said the move – currently planned in Scotland – is likely to be against European law.
She also said the Department of Health is in “ongoing discussions” with the Treasury on how alcohol pricing could be used to encourage safer drinking.
Milton questioned whether price changes could really change drinking habits, especially among problem drinkers, pointing out that 80% of alcohol was drunk by one-third of the population.
But she said that the new strong beer tax has already had an impact.
“There has been a response from the industry. Already they are dropping the alcohol strength to get below that duty level,” she said.
“There is no doubt about it, price can manipulate the market, so increasing duty on high-strength alcohol is not a bad idea, because for every litre sold there is less alcohol in it, which is a move in the right direction.”
The public health minister also backed local alcohol campaigns, saying they were likely to work best because consumption patterns vary from place to place, adding that there was “no one magic bullet” to solve alcohol abuse.