This song is related to An Binsín Luachra

Some hints that the English language versions may derive from the Irish language song are that it is referred to in Bunting's collection of 1809, earlier than the 1813 broadsheet mentioned above, and that a bit of Irish is retained in this English language version ending:
My heart you've captivated
On this place where the rushes grow,
And for ever I'll embrace you,
And your bonny bincheen luachara O!

(see Jim O'Carroll's 6 July 2013 message in the linked thread which goes on to say: A popular Irish song was sometimes given an English dress and issued as a broadsheet; and in this case I give the broadsheet version in place of a strict metrical translation of the original. The humble and unknown translators of such pieces knew Irish well, but their knowledge of English prosody was far to seek; and so, probably quite unconsciously, they imitated the assonance of their originals. To realise this to the full, one must bear in mind that the pronunciation is that of the Irish countryside—"daycent" for "decent", "crayture" for "creature", "plaising" for "pleasing", "aisy" for "easy", and so on. The internal assonance then becomes obvious. To take the third verse as an example:

I said, 'My charming crayture,
Be plaz'sing to me and kind,
This moment is the sayson
That engages my tender mind.
These rushes cost some labour,
'Tis plarn that the like do grow ;
Then grant me your kind favour,
Embrace me and ayse my woe'. "}

And in the message just previous to mine, Joe Offer could also have mentioned Rabbie Burns "Green Grow the Rushes o"