I always wondered about that.
Allen lost the top of his left index finger above the middle knuckle after catching it in a machine cog. He enjoyed inventing stories to explain the loss, which became a minor part of his act. One version was that his brother John had surprised him by snapping his jaw shut when they were children.
A further explanation he gave on his programme,
Dave Allen at Large, was that he often stuck his finger in his whiskey glass and it had been eaten away by strong drink. He also said it was worn away from repeatedly brushing the dust from his suit. One of his stand-up jokes was that, as a boy, he and his friends would go to see a cowboy movie at the local cinema, then come out ready to play
Cowboys and Indians. Staring down at his truncated finger, he would mutter, "I had a sawn-off shotgun". On his show he told a long, elaborate ghost story, ending with "something evil" attacking him in a dark and haunted house. Allen grabbed and bit the attacker, the studio lights came back up, and it was his own left hand.
You wake to the clock, you go to work to the clock, you clock-in to the clock, you clock out to the clock, you come home to the clock, you eat to the clock, you drink to the clock, you go to bed to the clock, you get up to the clock, you go back to work to the clock... You do that for forty years of your life and you retire — what do they fucking give you? A clock!