If you read your car insurance policy documents, you will find a section that says that your car needs to be roadworthy for your insurance to be valid. Without a valid MOT certificate, your car is not roadworthy and the insurance company have grounds to invalidate your insurance policy. This means that you can be prosecuted for driving without insurance and because your insurance policy will be considered void, damages to the other vehicle will not be covered as it would be regarded as if you were driving uninsured.
As you probably know, damages to your own car are not covered with third party, fire and theft car insurance (if your policy was valid that is) as it only covers third party losses. So overall, you could be fined for driving with no insurance and be liable for damages to the third party.