Liability?

Morning.

I'm looking for some advise on a recent accident, mainly who is to blame.

I went into the back of someone, which obviously 99 times out if 100 is my fault, my insurer says it's my fault but it's not as straight forward as that.

I was coming off a roundabout I wasn't too close to the car in front, but just as you leave the roundabout and pick up speed this car didnt, all of a sudden his car just stopped dead. I broke but couldn't stop in time.

As I got out and talked to him he said his car experienced a problem and just cut out, he didn't know what happened, he did however apologies and, on more than one occasion, admitted that the accident was his fault. There also was a witnessed who agreed I wasn't to close and there was nothing I could do.
The police came and took details and heard the guy admit liability.
So I thought this might be enough for my insurance company to at least try to fight my case but instead they wasn't interested, they just said my fault and the next time I spoke with them a few days later they are already talking to the other insurer admitting to them it's my fault. They just accepting it and not even trying to argue it, it seems like they just want it over with.

So I just would like advice on-
a) the accident, thoughts and feelings on whose to blame and
b) is there any way I can argue this with my insurer or challenge their decision?

Thanks for reading