i don't think that no MOT invalidates your insurance, it certainly invalidates your road tax though..
Why would it afect your tax, its a tax nothing to do with anything other than giving away more money. when you have no MOT it's a breach of the small print in your insurance, this means you have none, the car should not have moved......
you'd think that in this day and age, with the MOT's all being digital, that they'd be able to send out reminders the month before your MOT runs out..