I have just tried disabling my spare key, but there was no double flash of the led. Discovered that the whole of Voltermore 'Castle' is still within range of the car.
I tried John Ratsey's method but I'm not 100% sure its disabled.
I'd assumed the keys were the same as 'normal' cars , ie only using battery for a vhf signal when a button is pressed. But it seems the car transmits signals (presumably vhf) and the key uses battery power to respond.
With most cars the immobiliser uses a near field transponder chip in the key that doesnt need battery power. This may still be true on the Jazz. Ie if the key battery is flat and you get into the car using the emergency key blade, you should still be able to start the car by placing the key near the start button. - and drive to the nearest battery seller. But to be on the safe side I think I will keep a replacement Cr2032 button battery in the glove box.