I too have just found this page in the same away. I used to live in Newcastle upon Tyne and I am often reminded of the same lyrics when seeing pigeons but cannot remember where I learned them or where they are from and would be interested to know.
As I remember it "strut" comes in the next line to the ones you give. This may help you remember more.
This is all that I remember.

"The pigeons in the market square/walk upon the pavement there/Their feathers silver blue and green/ would make a garment for a queen/
They strut about and nod their heads....."

Best wishes from Ciencias y Artes Patagonia