I've priviously owned two minis (1990 and 1994) and had a similar problem, low on power and would cut out as I slowed down at junctions and lights, used to use the choke to keep the revs up to prevent this. Turned out it was only firing on 3 cylinders. Does it happen more in wet weather. Root of my problem was water getting into the distrubutor and/or a faulty lead on the plug (not sure if I have all the part names right).
Check out the forum on . The guys here know minis inside out and should be able to help you.