Prohibition was introduced in the UK as part of the Socialist Economic Improvements of the 1920s. It was basically an extension of the licensing laws introduced during WWI to restrict the sale of alcohol. The argument was that the consumption of alcohol was harming the efficiency of British Industry.
Of course, the aristocracy wasn't much affected by the law, as they could afford to take vacations in Europe or go on cruises to America. The measure was particularly unpopular in Scotland, with a number of villages conspiring to hide the contents of various distilleries from the British Revenue - as depicted in the 1950s film Whisky Galore!.
Basically, it came about due to a peculiar combination of Welsh Methodism and Socialism. It's hard to see how similar circumstances could arise in the United States.
Cheers,
Nigel.