There are several songs of this type. "I Will Never Marry" seems to have appeared in England as "The Lover's Lament for Her Sailor." Most versions end by the woman drowning herself. Several copies in the Bodleian Library, with date from ca. 1803- late 19th c. Here is one from ca. 1819-1844.

Lyr. Add: THE LOVER'S LAMENT FOR HER SAILOR

As I was walking along the seashore,
Where the breeze it blew cool, and the billows did round,
Where the wind and the waves and the waters run
I heard a shrill voice make a sorrowful sound.

Chorus:
Crying, O my love's gone, whom I do adore,
He's gone and I will never see him more.

I tarried awhile still listening near,
And heard her complain for the loss of her dear;
Which grieved me sadly to hear her complain
Crying, he is gone and I will never see him again.

She appeared like some goddess, and dressed like a queen,
She's the fairest of creatures that ever was seen.
I told her I'd marry her myself, if she pleas'd,
But the answer she made me, was my love is in the seas.

I never will marry nor be any man's bride,
I choose to live single, all the days of my life,
For the loss of my sailor I deeply deplore,
As he's lost in the seas I shall ne'er see him more.

I will go down to my dearest that lies in the deep
And with kind embraces I will him intreat,
I will kiss his cold lips like the coral so red,
I will close up his eyes that have been so long dead.

The shells of the oysters shall be my lover's bed,
And the shrimps of the sea shall swim over his head,
Then she plunged her fair body right into the deep,
And closed her fair eyes in the water to sleep.

Bodleian Collection, Harding B11(2238), ca. 1819-1844, printed by J. Pitts, London.

Belden printed a copy of "The Lover's Lament For Her Sailor" in his "Ballads and Songs Collected by the Missouri Folk-Lore Society, 1940 (1973) coll. in 1906 (but "sung to my mother over forty years ago...") in Missouri, p. 167-168.

The Traditional Ballad Index lists the song as "I Never Will Marry."
Belden says "See Roxburghe Ballads IV 397, where the author describes it as a modern reproduction of "The Sorrowful Lady's Complaint," a broadside from the Roxburghe Collection.