Actually, I'm going to have to be a terrible pedant here and point out that this isn't technically a
Monty Python sketch at all...
This sketch originally appeared on the pre-Python TV show At Last The 1948 Show, written and performed by John Cleese and Graham Chapman of the Pythons, along with Tim Brooke-Taylor (a friend of Cleese's from university who also appeared with him in the radio show I'm Sorry I'll Read That Again and later went on to appear on the TV show The Goodies as well as being a regular on I'm Sorry I Haven't A Clue on Radio 4) and future film star Marty Feldman.
Unfortunately 11 of the 13 episodes of that series were wiped by Paladine Productions (the company that made the show, owned by David Frost for whom Cleese, Chapman and Brooke-Taylor were all writers at the time), a shame as much of the Python style was developed in the show.
The Python connection with this sketch comes from the fact that many of the sketches from Monty Python's Flying Circus had no punchline or clear ending, and so for stage performances (as well as rewriting old material) they dug into their back catalogue. This was performed by various combinations of the Pythons over the years, and on their Live At Drury Lane album and Live At The Hollywood Bowl video it doesn't receive a special writing credit, so presumably Cleese and Chapman wrote the bulk of the sketch (if not all of it - they wrote the majority of the material in the show), but the performance by Cleese, Michael Palin, Terry Jones and Rowan Atkinson on the Amnesty International benefit concert video and album The Secret Policeman's Ball clearly label the writers as 'At Last The 1948 Show'.
This node brought to you by the Pointless pedantic corrections to w/us about comedy sketches team. You think you've got it tough? When I were a lad we had to node using our teeth for a keyboard, 25 hours a day, and when we got home dem bones would whip us to sleep with his belt...