OOOPS my bad!   I should have finished my research ... because
SOMEBODY ELSE wrote the text.

Yes, Arnold Dolmetsch says the words are by Izaak Walton,
and so do other editions of the song.
But I have just been set straight by the Encyclopedia Brittanica.

The words to The Angler's Song are credited,
if you know where to look, to
John Chalkhill (1595 - 1642).

After including "The Angler's Song" in his first edition of
The Compleat Angler,
Izaak Walton was kind enough,
for the printing of the third edition,
to identify "Jo. Chalkhill" as the author.