I think I asked about this song a while ago. All I know is:

There was a Chinaman
With pigtails spick and span
Ah hah ha ha ha ha
Who never would go out
When there was rain about
Ah hah ha ha ha ha
For rain, he used to say,
Washed pigtails all away
Ah hah ha ha ha ha ha ha
So indoors he would stay
On every rainy day
Ah hah ha ha ha ha

....
Just walk along the street
And him you're sure to meet
Ah hah ha ha ha ha
You're sure to find him there,
He walks without an air
Ah hah ha ha ha ha

The tune is George Formby-ish.