The problem comes when you open the car and then leave it for a short time before starting the engine and the immobilizer engages.
Are you sure it’s the immobilizer?
Is the car new to you, or have you had it for some time? And in this regard, when did this problem appear?
Once the doors are unlocked, do you leave it, without opening the door/s, or do you get in but don’t put the key in the ignition for a while?
When you first get into the car and put the key in the ignition (don’t turn it), does the “security” light on the instrument cluster stop flashing? And when the immobilizer appears to be on, does the light still flash or does it start flashing again?
When you try to start the engine, the engine does not start the engine at all, does it crank but the engine does not start, or does the engine start but stop a second or two later?
I seem to recall that some cars will reset the security system if, after the doors are unlocked, a door won’t open, or the key isn’t in the ignition, or something like that. Depending on the symptoms, I’m wondering if this car, being a UK version, might have something like that.