The timing could affect the idle / fuelling situation but not the points gap.
The more retarded the timing is the more you'll have to adjust the idle (faster - i.e. keep the butterfly's open more) in order to keep the engine ticking over.
The more the ignition timing is advanced the more you can wind back the idle (i.e. close the butterfly's off more). The car will also idle a little smoother and you'll have less run on BUT you have to be careful you do not advance the ignition timing too much. A mini motor can generally only handle about 32° maximum ignition advance and that should be all over by about 3,200 - 3,500rpm (or there abouts, where it reaches max advance depends on your dizzy curve).
It sounds like the carb on your old car was just whacked on with no thought for the needle. Your 1100 will not need as much fuel as a 1275 mini. I run GY needles in my 998 + 0.020" (rich 998 cooper) and I have heaps of adjustment, from really lean to just about spewing fuel out the exhaust.
A P.O. could have wound on more fuel (making it excessively rich) to try and cure it's poor drivability when it is cold. A little extra fuel can make you mini run a little better when it is cold. Before you start winding fuel on so that it runs better when cold......use the CHOKE - that's what it is there for
TBH, the more you talk about this car the more it sounds like the PO didn't know what they were doing, or if they did, they didn't care.