Richie here's the song that you mentioned:

THE BALLAD OF JACK THE RIPPER
(Words by Horace Phlange & James Home. Music by Thornton G. Roper)

It happened in Whitechapel in the year of '88,
When several naughty ladies met a rather gruesome fate.
Their murd'rer prowled the East End streets, and though it sounds absurd,
When they cried out, "Do you want a bit?" 'e took them at their word.

Oh, Jack the Ripper, 'e carved his way to fame.
Nobody ever saw him, but they all knew his name.
And when the mist is swirling thick around the Thames-side mud,
'Is ghost still 'aunts the silent streets, looking for some blood.

They found a woman's body in a nasty state one night.
The coroner 'e laughed and smiled to see the gory sight.
The p'lice thought this improper, as the street with blood was speckled.
"Who is that man?" the inspector asked. They answered, "Doctor Jeck'll."

Now Sherlock Holmes was on the spot and said, "I'll bet my shirt,
This villain Jack the Ripper must be the Prince Albert."
As he stepped back, the place went black, for all the gas lamps fused,
And even Queen Victoria said, "We are not amused".

A girl was walking down the street in Aldgate after dark.
Now Jack the Ripper menaced her, tho' only for a lark.
She fled into a barber's shop, not looking where she trod,
But it couldn't have been 'er night, because his name was Sweeney Todd.

Th'inspector was called out one night t'observe a special case.
The lady had been lacerated right up to her face.
When someone asked him, "Why d'you think 'e's made 'er such a mess?"
The inspector said, "She must have been a cut above the rest!".

Now Jack, 'e was a family man what lived wiv 'is old mum.
They sat down every night to supper when the day was done.
And when his muvver asked him, "Jack, fetch me a piece of tart."
'E said, "D'you want a change this week, or the usual ribs and heart?"


I think that the aforementioned "Sweeney Todd" is another song/recit of the same ilk.

The late Jake Thackray wrote quite a few songs, which although the humour tends to be sexual rather than violent, probably don't cross the line into "vulgar" ie "The Bantam Cock", "Sister Josephine", "Isabel Makes Love".

Dave Goulder's "The Sexton and the Carpenter" is probably one of my favourite gory folksongs.