Sorry to butt in but it sounds like your earth strap is probably frayed or loose. Mine was holding by the last few threads and was causing havoc, acting in the same way as yours. Also check the condition of the battery terminals. Good luck.
Well Gentlemen, I have the beast working properly again!

It was the ignition side of things this time! Wasn't getting enough of a spark, it seems. I replaced the spark plugs, capacitor condensor, put on new HT leads and hey presto the beast is back.
Good thing we have a Fiat 500 spares place (literally called 'The Spares Place') in South Australia.
The earth strap has been fitted on recently by me, and I know I cleaned all the gunk off it.
I don't know what the cause of the problem was, but probably a combination of all three of the components I replaced.
Thankyou guys for your time!

Now to replace the timing chain..
Alleyniki