It is not mentioned above, but this song is "parody" of
the chorus of "Jake the Peg" by Rolf Harris:

I'm Jake the Peg, diddle-iddle-iddle-um
With my extra leg, diddle-iddle-iddle-um
Wherever I go through rain and snow
The people always let me know
There's Jake the peg, diddle-iddle-iddle-um
With his extra leg, diddle-iddle-idle

Listen here: https://m.youtube.com/watch?v=imRaRW4ltOs&t=42s


Another Rolf Harris song "Tie Me Kangaroo Down, Sport" is used for
another bawdy song "Bestiality's Best Boys".