This is the song from my mother (Peggy Joyce Lodge) who was born in 1932 and grew up in Seer Green, Buckinghamshire. This would be from around the war years.

This is as I remember it:

There was a Chinaman who was very very stout
The servants could not carry him about
So they rolled him up to the top of the hill
and rolled him down with a Beechams pill

Ching ching chong chong chang chicaloram
Wiggy wiggy loram a wiggy wiggy wham, (this line really escapes me)
oko oko tiddly if fi ko
This is the way the Chinese talk