If Winston Churchill was a major functional alcoholic, he must have needed a crack support team to complete the enormous amount of work required of a head of state.
According to his daughter Lady Mary Soames what he usually drank was what she called his 'Papa cocktail' which was a splash of whisky in the bottom of a tumbler that was heavily watered down, which would then be consumed over several hours. His private secretary Jock Colville confirmed this. Colville described it as being 'like mouthwash' because it was very weak, suggesting it was as much a prop for Churchill's political image as it was a prop for him personally.
He was in his 60s when he became Prime minister in 1940 so by projecting this image of a man who could smoke countless cigars and put away drink after drink and still lead a country he was perhaps attempting to demonstrate that he had a robust constitution and that his age was not an issue for his leadership abilities.
The general consensus amongst historians of Churchill is that he may well have been alcohol dependent, since he reportedly drank throughout the day. This was a habit he would most likely have picked up whilst he was a young man in India and South Africa where alcohol would be added to water to make it safer to drink. However, people can be alcohol dependent without binge-drinking and Churchill seems to fit in to this category. It is still a form of alcoholism, but it's what we now would call 'high functioning alcoholism', where a person is able to consume just enough to satisfy an addiction but they can still maintain their work life, relationships and so on. It's not good because it often causes serious health problems in the long run, but it's not the stereotypical 'drink 'til you pass out' pattern we'd usually associate with the word 'alcoholism'.
Certainly there were times when he drank more heavily, especially at meals, but there's no accounts from those close to him of him having been intoxicated to the point where it was problematic (and lots of his close colleagues kept personal diaries where such accounts could appear) he also made many remarks that condemned drunkenness and drinking to excess.
http://www.drinkingdiaries.com/2012/04/11/interview-with-susan-elia/
http://www.winstonchurchill.org/learn/myths/myths/he-was-an-alcohol-abuser