The version above (from Hugh De Witt 1970) is almost a straight lift from:
The Long Trail, Brophy & Partridge (1st 1931/rev 1964)

It was Christmas Day in the Workhouse
Recitative

It was Christmas Day in the workhouse,
The season of good cheer.
The paupers' hearts were merry,
Their bellies full of beer.
The pompous workhouse master,
As he strode about the halls,
Wished them a Merry Christmas,
But the paupers answered: `Balls!`
This angered the workhouse master,
Who swore by all the gods
That he'd stop their Christmas pudden,
The dirty rotten sods.
Then up spake a bald-headed pauper,
His face as bold as brass:
"You can keep your Christmas pudden,
And stick it up your arse!"

A short variant ran:
It was Christmas day in the Harem
And the eunuchs were standing around
In strode the bold, bad Sultan
And gazed on his marble halls.
`What would you like for Christmas, boys?'
And the eunuchs answered `Balls!'

Pre-1914, part of the lore of the `working class', and popular
with the troops because it expresses the resentment of the
helpless against circumstances and against those with power
over them.

And IIRC the film Oh What a Lovely War had:

It was Christmas day in the Harem
And the eunuchs were standing around
And lots of lovely ladies,
Were lying on the ground.
When in strode the bold, bad Sultan
And gazed on his marble halls.
Crying `What would you like for Christmas, boys?'
And the eunuchs answered `Balls!'

AndyG