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.