Mixture too rich will reduce pinking (pre-ignition) rather than increase it (as far as I know).
I bet that the timing is now too advanced, like custard boy said, because somebody dialled-it-up when the vacuum advance was broken, in an effort to get the engine idling smoothly.
I think you're right to get hold of a strobe light and reset it yourself. From the Uno (series II) handbook, the correct advance is 3-degrees for the 1108cc (and only 2 degrees for the 999cc!) I think I have seen different advance specifications elsewhere, particularly in Haynes which lists the figures by distributor model.
This 3 degrees is without the vacuum advance - remember to disconnect it first! Also the engine needs to be idling as slow as you dare (but definitely below 1000RPM) since this is a 'static' advance, to be set without the centrifugal distributor advance coming into play. I use the timing marks on the flywheel under the black rubber cover on top of the gearbox, as they have nice clear pointers.
If the distributor seems to be at the end of its travel, check the cam timing (it's surprising how that can be wrong with little ill-effect).
Cheers,
-Alex