a 1981 car certainly won't have had a VIN plate when built. Mine (1985 4/4) has a chassis number only, which occasionally causes confusion with licensing and insurance folks.
I suppose it ought to be possible to work out what the VIN should have been if it had had one - the coding is more or less logical and encodes the manufacture, model information, place and date of manufacture, as well as the serial number of the specific vehicle. There's an explanation in the image below if it helps, but you'd still need the assistance of the Morgan factory to work out what the various sections would have been for your car. You shouldn't need to, though, since there would have been no VIN plate on the car when it was built.
Edited to add: apparently the below image is specific to North America. European standards are slightly different, though largely compatible. Wikipedia has a good article here
https://en.wikipedia.org/wiki/Vehicle_identification_number 
