
I'm sure the same law will apply to MOT exempt cars as in accidents where the driver of a modern car is prosecuted for bald tyres at the scene. It's all about roadworthyness, and in such a case your insurance is void.
Early days yet, but I'm sure if the insurance companies can find a way of not paying out they will. The new MOT exempt law will open the flood gates.
As for other countries without MOT, their insurances are tailored to suit the law of the land. I'm sure though that if you skidded, hit someone and killed them because you had bald tyres, you'd still be responsible for your cars condition.