In the USA Morgan M3W is imported as a motorcycle therefore the helmet laws of the state you are in must be followed or you will be given a citation.
While not required by law everywhere it should still be MANDATED BY COMMON SENSE to wear a helmet in a M3W as they have roll hoops. The problem with all roll hoops, roll bars, and roll cages in street vehicles is they are the ideal shape and size to become the "blunt instrument" of detective fiction fame and bludgeon you to death in an accident. In race cars this is avoided by padding bars, helmets, and quite complex restraint systems to prevent body parts, especially the head from contacting the roll bars. The hoops on the M3W are ideally placed to crack your skull if you are hit from the rear. There are many other situations where this could happen. Therefore, I must emphasize, even though I hate the uncomfortable, hot, stinking things WEAR A HELMET.