Having no MOT does not, I repeat DOES NOT, invalidate your insurance unless you are involved i nan accident, and a component that would have been picked up on the MOT (and would cause a fail) was the cause of the accident - IE a wheel coming off due to suspension issues, or a tyre blowing out due to it being down to the canvas.
I don't know why everyone thinks it invalidates your insurance.
We only check if you have an MOT if your car is stolen, or is a write-off. Even if it doesn't, most insurers will reduce the value of the settlement, but even the Ombudsman won't allow this if the policyholder challenges this.
I'm not sure what (if any) punishment there is for no MOT - someone like Ethel or New Judge would be able to put you straight