The legislation clearly allows people to use a car to make essential journeys - for example, to go to work (key workers) and to get shopping.
To date, I have not seen a list of what type of car you are allowed to use.
As said above, if you have convinced yourself not to use your Morgan, then that is your decision. I have yet to see any sensible or credible reason not to use my Morgan when I'm called in to work (the Mrs does all the food shopping - supermarkets make me angry)