It is my understanding, that certain segments of British society substitutes rhyming as a way to obfuscate speech, as a sort of game.
"Taking a piss" became "Taking a Micky Bliss" -Michael being the more formal patois, if you will. Taking a Micky (or Michael) got shortened over time to "taking a michael". In other words, an elbow in the ribs, a razzing, kidding, giving you a good-natured hard time.
And Bob's yer Uncle ~