THE term full monty comes from the demob suit soldiers were allowed after being demobbed from the army after the war. It consisted of a jacket,waistcoat and trouses. I think they were given some kind of voucher, to go to Montigue Burton the tailors, hence the name The full monty.
Montgomery was a famous british soldier in WWII who always had a full breakfast, whatever the circumstances, therefore the term full monty means the whole lot.
As haills points out, after being demobbed from the army, after the war, a soldier was given a suitcase containing a suit, shirt, shoes etc. Everything they would need to get them started in civilian life. These packages were made by Montigue Burton the tailors, hence the name the full monty.