There are two songs mixed up, above. Old King Cole had nothing to do with there not being a girl about/around.

That one went:

Ole King Cole was a Merry old soul/ bugger for a hole
And a bugger for a hole was he!
He called for his wife in the middle of the night
And he called for his fiddlers three..
Fiddle diddle dee diddle dee cried the fiddlers
Very Merry Men are we
There's none so fair as can compare
With the Boys of the Company/Ministry/ UCT/RAC

Further verses included

'He called for his wife in the middle of the night
And he called for his Jugglers three.
Throw your balls in the air cried the jugglers
Very Merry etc

.....
'And he called for his Tailors three
Thread it in and out in and out cried the Tailors
Very Merry Men etc....

I am sure one can concoct further verses of similar ilk.

Oh Yes! I forgot...

After 'There's none so fair as can compare etc' comes another bit which goes

"Oompah Doompah stick it up your Joompah
How's yer father? All Right!
How's yer mother? Half tight!
How's yer sister? She might!
When was the last time? Last night!

Old King Cole... continues....

Reverting to 'When there isn't a girl about (I prefer 'around', you can draw it out better) there were several other verses which we used to sing. In short:

Little Red Riding Hood
Went for a walk in the wood
Oh, what big eyes you got! What big eyes you got!
The wolf said Red, you aint seen anything yet,
he whipped his old bazooka out and gave her a helluva shot
Get hold of this, get hold of that,
Etc

Little Jack Horner sat in the corner
Looking at all the dirty pictures hanging on the wall
He stuck in his thumb
And couldn't find a plum
So he whipped his old Bazooka out....

Afraid that's all I can remember..

From 55 years ago....