The immobiliser in the system can malfunction, so in order to check this remove the fuse to this item and try again. You can run without this fuse with no worries, but of course it means the car is not protected as securely from attempted theft. I would also replace the battery in the key fob, that will also help turn the immobiliser off more "positively"
Secondly the 14CUX "Hotwire" system ecu is only controlling the fuelling of the engine. The ignition is handled by the distributor. It was not until the introduction of the Lucas SAGEM ("GEMS") system (about 2002/3 on the +8) that both systems were controlled by the ecu
Thank you for this information, Andy

The immobiliser has already been deactivated by the previous owner. But I will check, if there is still a fuse.
Check the connection between the ignition harness and the engine harness,a white two pin connector
Directly under steering wheel and on rear face of bulkhead (engine harness goes through bulkhead).
I had very similar problems on one of my +8 s (2000 4.6)
I had to cut this connector out of my car and replace with better (non time expired) connectors....
Thank you, Chris

Is you car a left, or right hand drive?