Former shadow Home Secretary David Davis has said he would prefer to see taxes on cheap supermarket booze raised rather than the introduction of a minimum price.
Speaking on the BBC's Question Time last night he said: "I wouldn't put prices up and give the money to the supermarkets that cause the problem. Why not get the money and spend it on nurses and police and doctors?"
Meanwhile Nicola Sturgeon, Scotland's Health Secretary, explained why the SNP had included minimum pricing as one of a range of measures to tackle alcohol in its Alcohol Bill, which was released yesterday.
She said: "I do believe a minimum price for alcohol will benefit society and this is broadly supported by doctors, nurses and police."
She added that the party had yet to put forward a recommended unit price for alcohol because it wanted to get support in principle from Parliament first.
However Labour's former Lord Chancellor, Lord Falconer said it was not clear the measure would lead to a drop in alcohol problems.
"I think we have got to find out if it is actually going to have an effect on alcohol consumption."
Scotland's Alcohol Bill also included plans to ban promotions and the sale of alcohol in shops to under 21s.
Meanwhile comedian Marcus Brigstocke and journalist Melanie Phillips both gave support to plans for a minimum price.
The Publican's Make it the Minimum campaign is calling for a 50p per unit minimum price to bring an end to irresponsible off-trade deals.