There's a Lincolnshire version of this song ,called "BETSY WALTON" - the verses I remember are:

Oh,Betsy Walton is my name -
I brought myself to grief and shame
Through loving one who ne'er loved me,
With sorrow that I now do see.

I did propose one Sunday night
To meet once more my heart's delight
On Humber's banks, where the billows roar-
We parted there to meet no more.

As token that I died for love,
There shall be seen a milk-white dove;
Above my watery grave to fly -
And there you'll find my body lie. . .