Be cautious, as low oil pressure will cause the alarm to stay on. If low oil pressure is the cause, then it will ruin the engine to run it!
Owners manuals are in the Morgan 38 Background, History, Reference section and include some electrical drawings.(link below)
If the alarm isn't shutting off, check the oil pressure and temp sending units, the alternator lamp (bulb) and that the alternator is working. To elaborate, that alarm isn't an ignition alarm, it is an alarm that something is wrong with the engine, either oil pressure, over temperature, or the alternator. It alarms before you start the engine because there is no oil pressure when it is not running.
Assuming that none of those things are wrong, then check the sensors for them.
Morgan 38 Background, History, Reference