Sounds like it has in fact been settled on a split liability basis because the third party paid your hire charges. Not uncommon on a roundabout accident.
Do you know if there is split? Even if it's 95% - 5% in your favour, it's still considered a fault claim for you.
You say your accident management company found you liable as well. Sounds like everyone thinks you're liable but yourself!
If you want to dispute liability, you need to take the third party to court and have the court determine liability. If you win, the third party insurer will reimburse your insurer all their expenses and the claim is registered an non-fault. If you lose, and the insurers have agreed say a 50-50 split and the court determines you were 100% liable, you're going to be a sticky spot with your insurer. It is for this reason you will probably find your insurance terms state that you agree to allow your insurer to settle all claims as they see fit - and thus they can agree liability as they see fit.
Once both insurers have agreed liability, I don't think there's anything you can do. If you sue your insurer, they'll almost certainly have a get out with the clause above.
If you think your insurers have mishandled your claim, you could look at going to the Ombudsman. Ombudsman will only usually look at complaints into procedural matters though - I very much doubt they'll look into making a determination of liability themselves.
I think you misread. The accident company did not find me liable for anything. The only reason they agreed to give me a hire car was in fact because they felt there was a big reason to suggest that I was not liable. Thats how they work.
I did write to my insurance company and they basically said that in your terms and conditions it is stated that it is up to us to decide liability and therefore you have no power to challenge this.
I did have legal costs cover, any chance I can use that to sue my own insurance company?
