https://www.nhs.uk/live-well/alcohol-support/calculating-alc...
Units aren't the only confusing thing here.
You need to read it in context. "Alcohol" is quite adequately defined at Licensing Act (Scotland) 2005 s.2: http://www.legislation.gov.uk/asp/2005/16/section/2
s.147 defines strength: "strength", in relation to alcohol, is to be determined in accordance with section 2 of the Alcoholic Liquor Duties Act 1979 (c. 4), thus "the alcoholic strength of any liquor is the ratio of the volume of the alcohol contained in the liquor to the volume of the liquor (inclusive of the alcohol contained in it)".
It's defined in such terms as that makes it easy to calculate - both strength and volume can be looked up from the label of the alcohol. The average person wouldn't know where to start with centiliters of pure alcohol in the beverage. You don't actually need to know what a unit is to calculate it, but it's 10ml of pure alcohol, or 25ml of a 40% spirit (standard sales amount). It'll be familiar to most UK drinkers.
> The minimum price of alcohol is to be calculated according to the following formula—
> MPU × S × V × 100
> where—
> MPU is the minimum price per unit,
> S is the strength of the alcohol, and
> V is the volume of the alcohol in litres.
It's hard to figure out, but I think "alcohol" actually means "alcoholic beverage" and "strength" means "percentage of alcohol in the alcoholic beverage". So with a MPU of £0.50 and pint (0.56 litres) of 3% alcohol cider, you'd have £.5 × .03 × .56L × 100 = £0.84. So it looks like the "unit" in "minimum price per unit" is "centiliters", although this unit is mentioned literally nowhere in the law.
It's a minimum price per centiliter of pure alcohol in the beverage. That's it.