Here are a couple of uses of hymn tunes that are clearly in the same tradition, and that appear in the University of St Andrews Students' Union Song book (1958; I was there at the time, and we sang them both):

THE PRESBYTERIAN CAT
(Tune: Crimond)

There was a Presbyterian cat
    Went searching for her prey,
She foond a moose within the hoose,
    Upon the Sawbath day.

The people all were horrifiet,
    And they were grieved sair;
And straightway led that wicked cat
    Before the ministair.

The ministair was horrifiet,
    And unto her did say:
"O naughty cat, to catch a moose
    Upon the Sawbath day."

"The Sawbath's been, frae days of yore,
    An institution."
So they straightway led that wicked cat
    To execution.

Moral
The higher up the plum tree grows,
    The sweeter grow the plums;
The more the cobbler plies his trade,
    The broader grows his thumbs.

FATHER'S PANTS
(Tune: Cwm Rhondda)

||: You must eat if you are hungry,
You must drink when you are dry. :||
You must rest when you are weary,
||: Don't stop breathing or you'll die. :||

||: Father's pants will soon fit Willy,
Will 'e wear them will 'e 'ell. :||
Will 'e wear them, will 'e wear them,
||: Will 'e wear them, will 'e 'ell. :||

"Ilkley Moor" is there too, but the tune is not credited.

In 1959 I brought "Father's Pants" to Cambridge, Mass., where for some years it was sung at every party of the MIT Outing Club.