There is no question in my mind that Henley's "Falmouth is a Fine Town" (see Ballad Index entry) was responsible for the shift from Rosemary Lane or one of its variants to the version called Ambletown. Here's my note:

"In fact, this was written in an Edinborough hospital in 1878 (published in Henley's "Book of Verses", 1888, and probably independently at an earlier date), and it was noted that "the burthen and the third stanza are old." These apparently are derived from either one of the versions of the song identified by Laws as "Rosemary Lane" (K 43) or a common ancestor. [For texts and tunes to several of these, search The Digital Tradition for (DT)"#319" or (Laws)"K43".]"

And here's the full text. Compare to Ed Trickett's version.

O Falmouth is a fine town with ships in the bay,
And I wish from my heart it's there I was to-day;
I wish from my heart I was far away from here,
Sitting in my parlor and talking to my dear.
   For it's home, dearie home--it's home I want to be.
   Our topsails are hoisted, and we'll away to sea.
   O the oak and the ash and the bonnie birken tree,
   They're all growing green in the old countrie.

In Baltimore a-walking a lady I did meet
With her babe on her arm as she came down the street;
And I thought how I sailed, and the cradle standing ready
For the pretty little babe that has never seen its daddie.
   And it's home, dearie, home,--

O, if it be a lass, she shall wear a golden ring;
And if it be a lad, he shall fight for his king;
With his dirk and his hat and his little jacket blue
He shall walk the quarter-deck as his daddie used to do.
   And it's home, dearie, home--

O, there's a wind a-blowing, a-blowing from the west,
And that of all the winds is the one I like the best,
For it blows at our backs, and it shakes our pennon free,
And it soon will blow us home to the old countrie.
   For it's home, dearie, home--it's home I want to be.
   Our topsails are hoisted, and we'll away to sea.
   O, the oak and the ash and the bonnie birken tree,
   They're all growing green in the old countrie.