My mum who came to the UK from India in 1948 sang this version:

In China once there lived a great man
His name was Chickeracka Chee Chi Cho
Chickeracka Chee Chi Cho Chickalorum
Conday Lorum, One a pack a one

His legs were long & his feet were small
This Chinaman couldn't walk at all

Chickeracka Chee Chi Cho Chickalorum
Conday Lorum one a pack a one

Oh toh toh toh, itti kitty catty co
Ittipie, ittipie, chi chi cho