If it were immobiliser related then surely it would not turn over?
On Rover T16 +4 it certainly will.
When I first got the car I mistakenly switched the immobiliser on, not only would the engine turn over, it would also start! Then immediately stop. once when away it would turn over without firing. Switching immobiliser on for 30 seconds, then off again allowed the engine to start.
KASPOMOG it may be worth checking the shroud around the ignition switch, sometimes the car bit of the system can become detached and slide down inside the steering column, giving the intermittent problem you have, or sometimes no starting at all. Worth checking for that - if it has moved a dab of superglue to refit the sensor near the ignition switch is all that is required... Good luck!