Any insurance company will try to find ways to avoid paying out.
Some policies specify the vehicle must be in a road legal condition to be insured on the road - this obviously includes road tax.
However, in this circumstance the vehicle would still be insured against fire and theft from private property.
Your car is still covered If it is not taxed, it will not be covered if it has no MOT, as part of your policy states the vehicle must be kept in a roadworthy condition, and without an MOT you have no proof of this.
I'm glad you posted a response kempie. I good friend of mine actually crashed their car on the motorway causing a 3 car shunt and writing off his own car. His insurance company asked him for his MOT Cert which he didn't have and then to add, they gave him what I thought was a more than generous payout for his car.
I was amazed that they still pay out without MOT's (not sure though if this is always the case).