Er ... sorry I'm late, folks!
Spike Milligan made a film in the fifties, where he played a country postman transferred to London against his will. He gamely tried to keep up his helpful practices -- like reading the letters to the old & infirm, and collecting the eggs and so on. One day io the sorting office, "they" were demonstrating a new sorting machine that was faster and more efficient, etc. etc. Spike worked faster and faster to keep ahead of it, and they had to keep speeding it up; in the end ... well, you can guess: I've forgotten what happened after that! No idea what it was called or anything else.