Heard this a long time ago from an Irishman named Jack Hopkins in Sydney.

It is a parody of "Mrs McGrath"

The bits I remember:
I'll tell you all a story that will give you all a shock
It's about two murders on the Ringsend Dock
The hero of the story was Biddy McGrath
She strangled two sailors with the straps of her bra

They tried to dose her with some foreign liquor
They tried and they tried but they just couldn't trick her
...

The gave first one such a belt in the head
That he fell in the river and he sank like lead
The other one came with a big "Aha!"
And she stuffed his gob with the rest of her bra
...

It's such a delicately romantic ballad that I would like to revive it.