This Guardian article is a rehash of a farrago (by the same author) that first appeared on 20th July in the Irish Times. The song that is being represented as an early version of Molly Malone bears no verbal or formal relationship to the familiar one about Molly and her wheelbarrow. It starts (first of three stanzas, the others have, 'Och it's how I'm in love etc.' as a chorus)

By the big hill of Howth,
That's a bit of an oath,
That to swear I am loth
To the heart of a stone;
But poison my drink,
If I sleep, snore or wink,
Once forgetting to think
Of our lying alone.
Och! it's how I'm in love,
Like a beautiful dove,
That sits cooing above,
In the boughs of a tree;
It's myself I'll soon smother,
In something or other,
Unless I can bother
Your heart to love me,
Sweet Molly, sweet Molly Malone,
Sweet Molly, sweet Molly Malone.

(From a W. Scott, Greenock, printed 8-page song book of around 1797)

There is nothing in this that corresponds with 'Cockles and Mussels' other than the phrase "Sweet Molly Malone". If that makes a version, I've lost every modicum of critical faculty that I ever had.

It is also being assumed that both deal with the same person. This too is untenable. There are at least two other songs with the name Molly Malone - one 'Meet me Miss Molly Malone' is of the early nineteenth century, the other 'Is your mother in Molly Malone' is an early twentieth century vaudeville song - Molly tells the young man inquirer that her mother is out and, when he asks can he come in and sit by the fire with her, is told that the fire's out too. Irish 8-page song books also hold a song called Molly McKeon, which, if the writer of the article knew about it, would no doubt be pitch-forked into the story too. If that was the case, we would still have a farrago but at least it would be a complete farrago.