While Minstrel Shows were quite popular in Victorian England (though in a country without a significant black population they had rather different social role from in the USA), my understanding is that they didn't overlap much with Music Hall.

Here's an account from the 1840s from this site:

In the 1840s a Music Hall singer W G Ross revised the song, changing the name to Sam Hall in the process. On 10 March 1848 Percival Leigh noted the following account of an evenings entertainment in an early Music Hall:

'After that, to supper at the Cider Cellars in Maiden Lane, wherein was much Company, great and small, and did call for Kidneys and Stout, then a small glass of Aqua-vitae and water, and thereto a Cigar. While we supped, the Singers did entertain us with Glees and comical Ditties; but oh, to hear with how little wit the young sparks about town were tickled!

But the thing that did most take me was to see and hear one Ross sing the song of Sam Hall the chimney-sweep, going to be hanged: for he had begrimed his muzzle to look unshaven, and in rusty black clothes, with a battered old Hat on his crown and a short Pipe in his mouth, did sit upon the platform, leaning over the back of a chair: so making believe that he was on his way to Tyburn.

And then he did sing to a dismal Psalm-tune, how that his name was Sam Hall and that he had been a great Thief, and was now about to pay for all with his life; and thereupon he swore an Oath, which did make me somewhat shiver, though divers laughed at it. Then, in so many verses, how his Master had badly taught him and now he must hang for it: how he should ride up Holborn Hill in a Cart, and the Sheriffs would come and preach to him, and after them would come the Hangman; and at the end of each verse he did repeat his Oath. Last of all, how that he should go up to the Gallows; and desired the Prayers of his Audience, and ended by cursing them all round.

Methinks it had been a Sermon to a Rogue to hear him, and I wish it may have done good to some of the Company. Yet was his cursing very horrible, albeit to not a few it seemed a high Joke; but I do doubt that they understood the song.'