hi there. it seems i have exactly the same problem with my ZX Reflex (K reg). You can stop it turn the engine off, and try to re-start it immediately, and occasionally it wont work (sep when damp or after long journeys). But some nice AA man put a live feed off the starter motor (i think?). Anyway if it wont start i put it in neutral, turn the key one click, and spark it off the battery!!drastic but effective. obviously this is not a long term soution, and not the safest one, but at the moment it is the best i have found.
let me know if you find a solution.