Oops! I presumed that it was aluminium.
With steel, a little more effort is probably justified.
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All good now. After googling every web site and forum in the known world I discovered that nobody has ever had this problem before, thus there are no diagrams or tutes on how to fix it. I finally went to Whirlpool, (which I avoid if possible because it seems to be run by little old ladies who don't get out much), and found a thread about a similar problem. The advice given in that case was to throw away the whole door lock and get a new one.
By that time I was ready to do just that. So, foolishly optimistic, I went to Bunnings. Turns out they had one.
Long story short I installed it and it works beautifully.
Great stuff.
So, now what you need to do is carefully pull the old one apart and see if you can find out where the “small metal block with a tiny spring” are meant to go.