Bish, bash, bosh - look at his dosh
There are earlier references in song titles (there is a jazz song “Bish Bash Bosh”, written by Barry Harris in 1962), and, according to The Guardian, in novels – a recent book review by Steven Poole states that the phrase “the bish-bash-bosh of freemasonry”, whatever that means, appears in a 1924 novel. I am not sure whether this means the phrase was in fairly wide use before Harry Enfield’s lighting on it, or whether he, like Barry Harris and the mysterious 1920s author, invented it independently of each other. The construction – three one-syllable nonsense words, with the noun changing from “i” to “a” to “o” – seems like a fairly intuitive one, if the examples above are anything to go by.
Spit spot, and off we go...
This type of vowel alternation is known as ablaut, and the construction of phrases using vowels in this sequence is known as "ablaut reduplication" or "ablaut-motivated compounding". According to this grammatical essay, the "a", "i", "o"/"u" sequence is the most common because these three vowels are the the "fundamental pillars on which the whole system of vocalisation has been constructed", with "i" at one end of the spectrum (at the front of the mouth) "o" or "u" at the other (at the back of the mouth) and "a in the middle. The sequence is not just found in English - the essay cited above notes that phrases like "piff paff", "piff puff", "bim bam", and "bim bum" are also found in German.
Some English irregular verbs also follow this pattern. Those with three vowels include ring/rang/rung, sing/sang/sung, drink/drank/drunk, sink/sank/sunk, and shrink/shrank/shrunk. Those with two include hang /hung, sit/sat, and spit/spat.
Middle English had even more examples of irregular verbs using ablaut, like chide/chode, climb/clomb and help/holp. But, as this essay by a group of Harvard maths graduates reports, these have gradually died out and been replaced by regular forms, with the least frequently used disappearing first. The paper predicts that "wed" will be the next to go, with "wedded" replacing it as the past participle.