Hang on though, I thought no MOT invalidated your insurance...
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Wrong, the 3rd party insurance cover can't be 'invalidated' its there to protect the third party from you doing stupid things like driving a defective car. They will pay out for any cliam that is accepted against the driver / last person to drive it if its parked regardless of the state of the vechiel/documentation
HOWEVER they will then sue you to reclaim the money they had to pay out because you breached the policys terms (usualy requiring an MOT, Tax, drivers license etc.)
An interesting point is that the last insurer of a car is always liable until you get a new policy in this regards. So if you cancel you policy, hit somebody, and injure them, your old insurance company can still be held liable to pay any compensation the third party may bring against the driver. AGAIN they will then sue you for there loss, and you could go to jail if you can't pay.
You used to be able to book in your car at an MOT station and drive there without an MOT as long as you were driving to a pre arranged booked test, and then drive it back if it failed to your own address for repairs. Obviously if it was declaired to be in a dangerous state and you killed somebody because of the defect your going to go down for a long time! - An the MOT tester will usualy call the police if you drive off in a car they concider to be dangerous aswell (dangerous does not cover things like fog light not working, screen washer sprayer out of fluid etc but does cover things like No brakes etc
However I was recently told that this option fo getting a car for which the MOT has run out tested by booking it in had been removed - I have not looked into this so if anybody does know if this is still the case (or not) I would be interested to know