As you can see most - but not all - drinks would become cheaper. This is because drinkers are grossly over-taxed at present (ie. the tax revenue greatly exceeds the costs to public services). Cider, by contrast, is somewhat under-taxed.
You can read the short briefing paper here.
I also wrote about it for the Telegraph...
A new briefing paper from the Institute of Economic Affairs shows what a fair system would look like. British drinkers currently consume approximately 50 billion units of alcohol a year. To recover the £4.6 billion in costs, there should be a flat rate of tax of 9p on every unit of alcohol sold. That would mean a higher tax on some strong ciders and a lower tax on other drinks. Overall, it would mean lower taxes, but even after this reform most of our drinks would still be more expensive than the European average. In the EU-27, the average duty on a pint of lager is 14p (we currently pay 52p) and the average tax on a bottle of wine is 44p (we currently pay £2.08).This is not the first time the idea of taxing alcohol by the unit has been suggested. Economic think tanks and temperance groups alike have called for the same thing. In 2011, the Institute for Fiscal Studies concluded that "it would seem desirable to treat different types of alcohol in the same way in the tax system" and, in 2016, the Alcohol Health Alliance called on the government to lobby the EU so that "drinks in all categories can be taxed according to their strength". This raises the salient point that EU regulation currently prohibits a sensible system of per-unit alcohol taxation. As luck would have it, this will not be an obstacle for long.
Do have a read.