bum-tit-tit
In 30 years I've never known anyone other than those who went to St. Michaels Primary School who sang this. Prove me wrong: "Bum Tit Tit! Bum Tit Tit! Turn the hairy handle now" "Bum Tit Tit! Bum Tit Tit! Hear the willy orchestra"
written by Ad*m *ucke*, approved by Log

There is also a form which includes "play the fanny banjo now"
written by He*en* Ma*innes*, approved by Log

It was 'plaaaaaaay, yer hairy banjo' round our way.
written by an*nymou* u*er, left hanging by Log

I've heard this, used to sing it at my primary school in Halifax, West Yorkshire.

'Bum tit tit, bum tit tit, bum tit tit, bum, play the willy orchestra, play the willy orchestra'

Complete with hand motions of hands on bum, then on chest, and then the hand motioning some sort of bend penile trombone. Oh what we sang before we understood why.
written by an*nymou* us*r, left hanging by Log

In Manchester we said "Bum-tit-tit,Bum tit-tit, play the Willy Banjo" You obvioulsy went to a Posh School! We also did Milk, Milk, Lemonade, chocolate round the corner, press the button, pull the chain - out comes a chocolate Puffa Train"
written by Ma*ia Br*ok*, disapproved by Susan

In Manchester we said "Bum-tit-tit,Bum tit-tit, play the Willy Banjo" You obvioulsy went to a Posh School! We also did Milk, Milk, Lemonade, chocolate round the corner, press the button, pull the chain - out comes a chocolate Puffa Train"
written by Ma*ia*Bro*ks, disapproved by Susan

Yeah, our version was "bum-tit-tit bum-tit-tit, play the little banjo-man"
whith an accompanying hand gesture that suggested masturbation. The "banjo" imagery was always a bit of a mystery, but girls seemed to get offended by it, so we we did it nonetheless.
written by Da*e Pal*er, disapproved by Ponky