Thanks Bruce.
I've progressed a little since yesterday.
Took the capacitor out and boogied on down to the local mower place. Very helpful chap there tested it and said it looked ok... Not ruling it out at this point but it's a good sign!
The points and capacitor are installed under a plastic cover on this mower and even though the outside of motor is disgusting, under the cover was very clean.
The Mower Guy said he'd seen problems with the actual HT lead on this type of magneto before, and suggested I check that the lead is ok, and to be on the safe side, try re-terminating it in the coil (which I did). Also checked the coil for continuity - looks ok.
Going to re-install the coil/e-core with the correct gap tonight. No, I didn't clean the points with emery paper - saw the note about not doing this in the manual (why not??) As I said before, the points look to be brand new...but I'll dress them anyway and see how it goes. If still no joy, I'll see if my local guy would be able to test the coil and go from there. As an aside: I saw a note in the manual that said the coil is unique to this ignition system and can be differentiated by the brown plastic cover. This is the coil I have - is the note still valid? Do I need to make sure the replacement is *also* brown?
I will not let this %^@!!! thing beat me. Meanwhile, the grass is turning into a pretty fair imitation of tropical jungle.

BTW: Had a laugh at the forum software. In my original post above there's a word [censored]!? I'd said "turned off the fuel cock and waited"...
Cheers and thanks again - Andrew