First, alcohol is inelastic with respect to price. This is why, like tobacco and petrol, there can be such huge taxes with very little impact on consumption. In particular, those dependent on alcohol, like those dependent on class A drugs will absorb the price hike by reducing expenditure on other things (food and clothes for the children), rather than reduce consumption.
Second, the minimum price would raise the price of all alcohol, with the impact of squeezing shifting demand away from the cheapest varieties. Those who buy premium beers and £5 a bottle wine will see the price of their tipple rise, though maybe not quite as much a the white cider and the cheapest plonk. It is only the drinkers of 25 year old malt, first estate Chateaux Laffite and the older vintages of champagne and port who may not notice the difference.
Third, is to combine these two factors and see who gains. Consumption overall will drop very slightly, but the profit margins on 95% of the market will increase substantially, with the worst of the cut-throat competition eliminated. Add to that proposed restrictions of advertising, that will eliminate potential competition and the biggest gainers will be the retailers and the drinks companies. The losers will be the 99% of consumers who do not reduce total spend on alcohol.
Excessive alcohol consumption is a cultural, not an economic problem. From 1900 to 1930 consumption fell by 70% due to two factors – the temperance movement and the elimination of young men, the heaviest drinkers, in the Great War. It is only by a cultural change that consumption will fall. See my earlier posting here. A small change in price will not save thousands of lives per year. Any economic model that predicts this is flawed.