It turns out that I gave much of the above information in another discussion a while back (this song does come up rather often, with many of the same misconceptions being repeated by different people): RE: Water is wide: song history request. I mentioned there that Pete Seeger learned his set from his sister Peggy; she probably got it from one of Sharp's books, either directly or at some remove. He added a verse from somewhere or other. I also went into more detail on the Somerset text published by Sharp.
Having also re-found Bruce Olson's very useful post on the song (Re: "Waly waly", "The Water is Wide" and "Love is Pleasing") I can add a little to my previous comments in this thread.
The Water is Wide verse turns up in The Ripest of Apples, a song collected near Portland, Maine (no date or source given), which appeared in The Journal of the Folk Song Society, vol.I no.2 (1900). Whether it's a bona-fide member of the family or just a fortuitous collection of floating verses is hard to tell (it's usually classed separately nowadays), though J. W. Allen, (Some Notes on "O Waly Waly", Journal of the Folk-Song Society, vol.7, no.3, 1954) considered it part of the group. He also printed another song from the US, Maggie Gordon, which contained the Water is Wide verse; I haven't seen the article yet, but will try to pick it up in the next few days .
Bruce posted the Maine song here: The Ripest of Apples. Also in that thread is a similar Ulster set with the same title, from Songs of the People: the tunes are clearly related to each other, but not, so far as I can tell, to the English song. A form of the Water is Wide verse appeared in a number of broadside versions of I'm often Drunk and Seldom Sober in first half of the 19th century; A.L. Lloyd considered these to be mere collations of floating verses. A number of examples can be seen at Bodleian Library Broadsides; here is one:
I'm often drunk, but seldom sober ("The sea is wide and I can't get over...") Printed by Liptrot of St. Helen's, date unknown.
It's perhaps worth noting here that the Canadian song, Peggy Gordon, contains some of the material in the broadside.