Your insurance is NOT void with no MOT and is certainally not void with no tax. Your insurer wont care whether the car is taxed or not however as far as no MOT they will have to deal with any third party claim (Road Traffic Act 1988) and will make a case to case decision as far as your own car is concerned. The usual policy stipulation is that the vehicle must be roadworthy which is not the same as road legal. Ive worked for insurers for over 10 years and Ive seen clains paid with no MOT and claims avoided for a bald tyre. Condition is more important than documenation to your insurer. Bear in mind as well they will normally only ask for vehicle documents when dealing with your car as a total loss.
That said dont drive without an MOT its a criminal offence and I believe the police have the powers to confiscate vehicles. If they catch you could be looking at a fine, theyll no doubt check your car over, how confident are you that they wont find something?