British Library; The Workhouse Boy was clearly popular, being published in the 1840s in many different editions around the country, from London to Birmingham and Preston.
The music borrowed here is The Mistletoe Bough, a dramatic song published in 1830 about a bride who dies on her wedding night by accidentally locking herself in a chest.

The cloth was laid in the workhouse halls
Greatcoats hung on the whitewashed walls
The paupers all were blythe and gay
Keeping their Christmas holiday

Chorus:
And we all of us say it
And we say it with sneers
Jamie's been murdered by the overseer

You can find the grim conclusion in the DT above.