I recall the parody from an old 'Oldham Tinkers' album. Fuller lyrics than the stanza posted above have been posted to the rec.music.folk newsgroup. The Oldham Tinkers sang most of these - in a children's songs medley, I think:

CHARLIE CHAPLIN

And the moon shines bright on Charlie Chaplin
His boots are cracking for t' want of blacking
And his old fusty coat is wanting mending
Until they send him to the Dardanelles

Charlie Chaplin, meek and mild, swiped a sausage from a child
When the child began to cry, Charlie socked him in the eye

Charlie Chaplin had no sense, he bought a fiddle for eighteen pence
And the only tune that he could play was Ta-ra-ra-boom-de-ay

Charlie Chaplin went to France to teach the ladies how to dance
First your heel and then your toe; lift up your skirts and 'round you go

Charlie, Charlie, chook, chook, chook, went to bed with three white ducks
One died, Charlie cried, Charlie, Charlie, chook, chook, chook

One, two, three, O'leary, I saw my Auntie Sary
Standing in the door, O'leary, kissing Charlie Chaplin
--Stewie.