Similar version to one posted above.
Hull 1950s street rhyme

Chinky Chinky Chinaman bought a penny doll,
Washed it, dressed it, called it Pretty Poll,
Sent for the doctor, doctor couldn't come,
Because he had a pimple on his bum, bum, bum.

I may have confused 2 rhymes here. It was along time ago and senility is creeping in.