Does anyone know what the laws in the UK are regarding riding these mopeds:
The first one which will trip you up is that you'd probably never get it registered, start here to see whether it's even possible to get a vehicle like that approved.
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.
The first one which will trip you up is that you'd probably never get it registered, start here to see whether it's even possible to get a vehicle like that approved.
You would need a category A or B licence , i.e. a full car or motorcycle entitlement.
You don't have to wear a helmet to drive a tricycle.