I don't recall my source for this, but it will most likely have been one of my friends at the late lamented Heritage Society in Oxford, circa 1959. (Bruce Carter perhaps?) I'd completely forgotten the song until now, but have just come across it in my scribbled notes from that era, and then found this thread.

Tune - My Bonny Lies Over the Ocean.

Though I've just given birth to a heifer
And of pride and of milk I am full,
It is sad to relate that my lacteal state
Was not brought about by a bull.

Bring back, bring back, oh bring back my old fashioned bull to me
Bring back, bring back, oh bring back my old fashioned bull.

I've never been naughty, I swear it,
In spite of the calf I have borne;
By Farmer Brown's tractor I'm virgo intacta,
I've not had a bull by the horn.

Bring back, etc.

How dreary the farmyard and meadows,
The shipper looks gloomy and grey,
Now the one bit of fun in the year's dreary run
Has by science been taken away.

Bring back, etc.

If what I have heard is the truth, Sir,
Unnatural though it may seem,
A cow's female passion is all out of fashion
And bulling is just a wet dream.

Bring back, etc.

Now I know that a farm is a business
In which we must all pull our weight,
And I'd pull and I'd pull for a strongly built bull
But this phony arrangement I hate.

Bring back, etc.

It mustn't be thought that I'm jealous -
There are things that a cow shouldn't say:
But those Land Army tarts who handle our parts
Still get it the old-fashioned way.

Bring back, etc.

The title I have is the punchy-sounding "Lines written by a Disgruntled Cow on the Subject of Artificial Insemination".

I agree it looks like it must have a WWII origin.