The Prime Minister, a champion of minimum alcohol pricing, has insisted this “wouldn’t really affect family budgets, but would deal with this problem of very aggressive deep discounting and some binge drinking”.
However, he is facing opposition over the plans from a number of senior Tories, who fear it will hit moderate middle-class drinkers with higher prices. Some Liberal Democrats also see the plan as “illiberal”.
There are also fears it could run into legal difficulties with the European Commission, which has raised concerns about Scotland's plans to introduce similar measures.
The Home Office is still officially consulting on the plans but the Government appears to have been slightly cooling on the idea, amid persistent worries about the cost of living.
Even though Mr Cameron has publicly backed the policy, it is still possible that the price per unit could be revised downwards or scrapped entirely and replaced with voluntary agreements with industry.
Miles Beale, chief executive of the Wine and Spirit Trade Association, said the Mayor is right to point out problems with the plans.
“Under the Government’s plans to set higher alcohol prices through minimum unit pricing it will be the majority of responsible drinkers who will be asked to pay more," he said.
"Pushing up prices to deal with the actions of a reckless minority is unfair. Ordinary people looking for value for money in their weekly shop should not be labelled as binge drinkers."
Research carried out by Sheffield University for the Government has showed that a 45p minimum would reduce the consumption of alcohol by 4.3 per cent, leading to 2,000 fewer deaths and 66,000 hospital admissions after 10 years.
The number of crimes would drop by 24,000 a year as well, the research suggested.
However, the alcohol industry has disputed these findings. A new report by the Centre for Economics and Business Research, commissioned by the industry, claimed the official figures are unreliable and based on old data from 2006 which have already been proved wrong.