David Cameron is continuing to commit to a policy of minimum alcohol pricing of 45p per unit, despite many Cabinet members opposing the move.
Both Liberal Democrat and Conservatives are thought to be against the plan, with critics branding it illiberal.
Meanwhile, a report commissioned by brewer SABMiller suggested that a minimum price would cost consumers £659 million per year and do little to hinder binge drinking.
"A minimum unit alcohol price of 45p has a negligible impact on hazardous and harmful drinking levels among the richest 20% of households in the UK," said the centre for Economics and Business research, which carried out the report.
"Yet higher income households exhibit higher levels of combined hazardous and harmful drinking than lower income households."
A ten week consultation is currently under way to look into the feasibility and possible impact of the move, but it is understood that home secretary Theresa May and her Liberal Democrat junior minister Jeremy Browne are opposed.
If passed, the measure would see the minimum price for a bottle of wine set at £4.20 and 90p for a can of beer, but the rise in prices would not be collected in taxes.
The Scottish parliament passed a bill introducing a minimum unit price in May this year, but that is currently under judicial review after a legal challenge by the Scottish Whiskey Association (SWA).
They argue that the policy breaches EU trade rules by distorting the drinks market and claim it will cost the industry £500 million a year.
The outcome of the review will be key, as if it is found to be in breach of EU trade rules then it will bring an abrupt end to the government's plans to introduce minimum pricing in England and Wales.