Have heard this song at Sidders in "The Newt" and in the Ringwood Folk Club, (Hampshire UK). The chorus, if my memory is correct, goes:
      One leg up and one leg down like a cockney sparrow
      Flying over Piccadilly witrh me bow and arrow.

    Can anyone supply the lyrics please.

Being an ex Londoner, born in Plaistow many, many years ago, this song 'tickled me fancy'.