Churchill was a great man, but had real issues nontheless. During WWII, he underwent fits of debilitating depression. He probably needed alcohol as a pick-me-up to face the day.
In one of Churchill's better biographies -- The Last Lion, I believe -- the author mentioned that Churchill was rarely, if ever, completely sober during his entire adult life. He wasn't a drunkard, but he always had alcohol in his bloodstream.
As for his depression, he called it his "little black dog," that followed him around his entire life. Depression seems to be the mark of many great people.