Okay, all much simpler than I first imagined. Reasoning that the stronger the arm is trying to pull the ball out the socket the more friction there is on the arm side of the ball and connecting socket which increases the friction and consequently the mirror is less loose.
So thinking the right angle joint between the arm and the ball shaft is no likely to be one piece I decided to try getting access to it by cutting out the plastic cap by slitting down the circular recess.
Once that was out the way it was obvious that the arm and ball shaft were held together by a 10mm nyloc.
So by sliding some tubing on the ball shaft I created some tension between the mirror head and the arm which had the effect of increasing some additional tension and friction in the ball and socket.
Just a quick tidy to do.