Rover 216 issues ?

What is making my car cut out all the time in the morning. I noticed it this morning the car kept cutting out about 5 times in two miles only when i slowed down or stopped at a junction. I then stopped in a petrol garage to get some petrol. When I went to leave the immobiliser came on and since disarming that the car drove perfect. I should say the car has only done this once before but the immobiliser thing didn't click in my head. What could I do to stop this from happening?
Second point is the car keeps hunting when idling. You can feel it in the car and see it hovering between 950 and 1100rpm. I have changed ALL filters and cleaned throttle housing.

Any help would be appreciated