As a general rule you would be to blame as you hit the other car from behind....HOWEVER I feel your pain 100% because far too many people brake to a complete stop at roundabouts, junctions etc when there is no need to and I have found myself quite close to the car in front on a few occasions myself over the years.
I hope it gets sorted out quickly and your car is repaired rather than written off.
I had the same last August. Coming off of the slip onto a main road, the car in front went, i looked left to see if anything was coming, saw nothing and edged forward (you have to do this since people have a habit of coming from the middle to inside lane as you pull out there). Next thing I know I'm in the back of a car I thought had left.
Looked over the dash cam footage, and she went and then slammed the brakes on hard for no reason whatsoever. Because of the dash cam footage the insurance co's put it down as shared blame, even though legally speaking it would have been my fault for going into the back of her. Having partial blamed saved me a good hundred quid when it come to renewal time.
I tried to argue the toss. My insurance company (Admiral) wouldn't even entertain the idea because it isn't worth the hassle to them.....
Who insured the other party? If the insurer was unwilling to argue, then the chances are they had the same insurer (they'd be paying for it any way, so why bother with extra paperwork).
That said, if the insurance company refuses to throw out injury claims when you have evidence she was not wearing a seatbelt, threaten to take them to court. They have a legal contractual obligation to work in your best interests. I imagine a threatening letter is all it'll take.