As calum says. The rectifier must have gone.
I have gone through a few.
Morgan released a solution in 2013. If your car is 2013 or 2012 then you need to get the wiring schematic upgraded to the latest specification.
just because a car was serviced at a morgan dealer does not guarantee it has been done.
It was a big thing in the firat two years but the lack of chat on here aboht it shows how the fix must be doing.
You can tell if this has been done by looking how many grounding wires come out of the bottom of the rectifier and connect to the chassis. They are about 6 inches long these wires. If there is only one then you do not have the latest spec.
Transient voltages will have fried your rectifier and it will have to be replaced. This will keep happening until you upgrade the wiring. Take a picture of the rectifier if your unsure.