What voltage do you get and do you see the battery voltage with engine stopped?
Your assumption the regulator has failed is probably right but usually the light staying lit is a sign of too few, rather than too many volts. The reason I ask about the battery voltage is an alternator that has become electrically disconnected can soar in output voltage.
As for where to get one, just about any proper parts shop but as the Morgan installation may differ from other cars with that engine, make sure the new one has the same mounting points and spaces.
