I dont think Inky Pinky Ponky was chanted as a tease, just sharing a rhyme, when we should have been getting on with our work.
All the (English) Nursery rhyme books, had London bridge in (also sung on the 'wireless' on Listen With Mother)
London Bridge is broken down
Broken down
Broken down
London bridge is broken down
My fair lady

How can we build it up again? ....

Build it up with (something and straw)...
- and straw will be washed away...
Build it up with silver and gold...
Silver and gold will be stolen away...

Build it up with stone so strong..
Stone will last for ages long
My fair lady.