Several folks have written to say that the sketch that was this morning's video link — The Four Yorkshiremen — appeared on At Last, the 1948 Show. In fact, it apparently appears on this DVD which I have here but haven't watched yet.
If that's its point of origin, that helps narrow down the question of its authorship. The writing credits for that program were for its stars: Marty Feldman, John Cleese, Graham Chapman and Tim Brooke-Taylor. Tom Wolper sent an e-mail saying that Eric Idle performed the sketch on his recent Greedy Bastard Tour and identified it as one written by Feldman for At Last, the 1948 Show. Good to know.