Is it still allowed to ride that without a helmet?
Yes, in the UK you don't have to wear a helmet to drive a tricycle, whether it's purpose built or a converted motorcycle. You might want to wear a helmet though, as getting whacked in the face by 30mph insects isn't fun.
It is a moped with a dutch registration and license plate, combined with a dutch owner.
Is it still allowed to ride that without a helmet? (gov.uk doesn't even give me any assistance on that part)