According to the FA site it was 1981 and it was then modified to the version you're referring to in 1983.
Have a look on this site;
http://www.fifa.com/classicfootball/history/law/historylaw2.html
Thanks Disorganised, for all your effort and research, but I somehow don't think that's the rule we're talking about.
Law XII - Fouls and Misconduct -1983
Introduction of the four-step rule:
...from the moment the ball comes under his (the goalkeeper's) control, he takes more than four steps without releasing the ball into play and - having released it - he touches the ball again before it has been touched or played by another player...
In fact, I don't know what this is referring to as, if I read this correctly, it is saying that after 4 steps the ball has to be put into play and if he touches it again before another player (from either side apparently) it is a foul. Have you ever seen this rule in effect?
The rule I am talking about is when a goalkeeper gets the ball in the box, he can only move with the ball in hand by bouncing the ball every 4 steps. (I also remember that an opposing player was allowed to touch the ball when it is momentarily on the ground while being bounced. Crazy, I know!) The goalkeeper could, technically, run all round the box using this method for as long as he wanted to.
I gotta feeling it was way before the 80's. Just look at some of the YouTube footage from the 70's and you'll see this bouncing rule was not in effect then. Curiouser and curiouser!