Ah, third party property/fire/theft does not cover YOUR vehicle, only a third party. Seeing as you are not in the wrong (ie in need of covering the cost of another vehicle) you will be lumped with the repairs to your own car, unless you get the other party (or its insurer) to cough up. Your insurer ain't going to help you. Thats why we should all have full comp.
Your best bet right now is to contact this third party that caused the accident and get all info from them and give them a nudge to repair your car. My guess is, they know you're only on third party cover and they will just ignore you and hope you go away. Try to get the name of their insurer if you can, then contact their insurer and explain the situation and you want your car repaired.
Document EVERYTHING. While its fresh in your mind. Take pics and all. I feel you're going to head to the Courts if the third party don't play ball.