But I've just heard it today in Radio Active, the 80s Radio 4 comedy, series 1 episode 5, first broadcast October 6th 1981.
So JC might have borrowed the joke from them; or perhaps he wrote it himself prior to that date, let them steal it and then refrained from using it himself for another 2 years; or perhaps they both heard it from an an earlier, as yet unknown source (Pete Best?)