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Ok, Thank you very much for your response.
It seems I was a little short-sighted as I was convinced the term had some kind of cockney rhyming slang definition (eg. don't give a Tom-tit = don't give a s**t; let's have a butcher's = let's have a [butcher's hook] look.)
I was of the impression that the term don't give a monkey's, left a counter rhyming word to one's imagination (such as don't give a monkey's xxxxxx, which would presumably rhyme with something of the f**k persuasion!) It now seems my infinite folly has driven me to despair only to find that there is no ******* slang definition after all! Ignorance is bliss? Tat!
I shall now pass this nugget of wisdom on to my collegues who are all equally perplexed!
Does anybody else say the phrase assuming it to be of rhyming slang origin?