Taffy,
I was just looking up my notes on this problem and a possible cause is the MAF. Not sure if you have already lookded at this but if not the Air flow sensor MAF could be an answer. Owners of the S1 have experienced engine cutting out at traffic lights, going into limp home mode etc when this is faulty. Accessed through the cowl and a standard BMW part, £100 cost was mentioned.
Also Viper mentioned in a post some time ago about Brian Millers "stent" idea fitted to the rubber tube air supply which had collapsed thus causing the MAF to fail.
Let me know if you solve the problem
