If the NCT is out of date then the insurance company can say that the car was not roadworthy. You are responsible for the nct so by allowing it to run out, you have not taken due care to ensure the vehicle remains roadworthy.
In light of this, it is hard to see any of the insurance companies paying out if you crash.
as so much of the nct stuff has nothing to do with roadworthiness, afaik the insurance companies are not as bothered about it as the nct people might like