This seems to be the original song that Mark Graham was parodying. It looks like they could be sung to the same tune.

Lyrics below copied from Paul Brady's web site. Brady sings this on his album "The Liberty Tapes."

JACKSON & JANE
(Words traditional, music Paul Brady)

You Monaghan sportsmen I pray you draw near,
To a few simple verses you quickly shall hear,
It's the deeds of a hero that lives near Ballybay,
And they call him Hugh Jackson, I hear people say.

His mill, kilns and barns, they do cut a great show,
And his cloth to the North and the City does go.
At bleaching and lapping he does beat them all,
And his cloth was first approved of at the Linen Hall.

And more of his praises I'm going to explain,
So if you will assist me, I'll sing about Jane,
Search Ireland all over from Cork to Kildare,
And you'll ne'er find a match for Hugh Jackson's gray mare.

He went to the stable, to the mare he did say,
'The hour is approaching and we must away,
For a cup at Cootehill you have twice won with fame,
And this day we are challenged, and you must run again'.

She turned in her stable, 'Kind Sir, don't you know,
This cup is my own and I won't let it go,
For twice I have won it and I mean to do still
And we'll roll it in splendour from the plains of Cootehill:

The Jockeys were mounted and all in a row,
And if you had a' been there when off they did go,
The bets they were makin' ten guineas to four
That the cup back to Creeve would return never more.

When Jane she heard this, well, her mettle did rise,
Over hedges and ditches like lightning she flies,
And with aloud 'neigher' these words she did say,
You Bellamont sportsmen, I'll show yous the way'.

When Jane and her jockey were half round the course,
Miss Jane and her jockey began to discourse,
Said Miss Jane to her jockey 'Kind Sir let me know,
Where are my opponents or are they in view?'

He turned in the saddle and he cast an eye round,
'As for Squire Adams, he lies on the ground,
I'm afraid that poor Curry by Spanker is threw,
And the rest of your opponents they are not yet in view.'

When Jane she heard this, she went in at a race,
And into the scales the balance was laid,
The hall was surrounded for Jackson & Jane,
And the cup went with honours back to Creeve once again.