Hannes, it could be anything. Sometimes this coil around the lock is defective. Can you see the LED of the immobilizer, which (on my, 4/4) unfortunately is not on the dashboard but shines in the middle of the footwell at the very front end? You can only see it with a mirror or if it is dark, it shines indirectly. It should blink continuously when the key is removed and be completely off or on in the ignition position (my memory is weak here). Other TMs here can remind you more precisely how the LED behaves in which phase. This way you or a professional can see if the key is recognized. I would test all fuses that affect the startup process. Fuel pump, starter (relay?) ignition etc. Because maybe the immobilizer is not the reason.
I googled briefly, at least on a Ford you can't just remove the immobilizer. It is part of the vehicle registration. Whether it is different in the Morgan, I don't know. The immobilizer is in the Morgan 4/4 in the small black separate plastic box, which lies on the control unit in the metal container with the fuses.
