Brian,may think there is a similarity in tune. so?/...
the lyrics of on one april morning, and the transportation/broken token ballad... all around my hat are very different.

The similarities in the tunes are pretty obvious, Dick. I agree that 'April Morning' is a substantially different song from the Cockney transportation broadside, but the 'Green Willow' broadsides mentioned above - which sometimes identify the protagonists as William and Pheobe, and sometimes don't - include all the 'April Morning' verses together with the 'Hat' chorus.

The 'Hat' chorus is also found in some versions of 'The Nobleman's Wedding'. This was my point - the chorus got attached to at least three different sets of words (probably more) and the tune often went along with it.

None of the links in my 2011 post now work, so I'll try to restore them when I have a few minutes.