But, no MOT means no insurance.
I agree the police will not do anything if you get the MOT done promptly, but if you have an accident your insurance company may say your insurance is void.
I can't count the number of times I reply to these sort of questions - not a go at you dippydoo!
If you have no MOT, this DOES NOT mean that your insurance is invalid.
This would only POSSIBLY be taken into consideration IF you had an accident, and IF a component that would have been picked up under the MOT test failed, causing or contributed to the incident - ie brakes, tyres, etc.
Otherwise, it makes no difference whatsoever (same applies for having no tax).