Go to a solicitor specialising in RTA claims:
BMW will probably be able to help as part of their accident management service.
The legal eagle will be able to tell you whether they could fight this case or not. If they are prepared to take it on, that means they are assured a full recovery, ie that precident in that kind of accident is set and the third party can be blamed 100% for the RTA.
I had an accident years ago in Congleton.
I changed lanes well before a set of lights that then turned green. As they turned, some kids on bikes crossed the road, prompting the two cars in front of me and myself to brake sharply. The car behind me ploughed straight into the back of me.
The driver stopped, and did not accept liability. She claimed that I had cut in front of her, reducing her stopping distance. I asked the insurance assessor who took photos of my car to assess the angle to impact to see if it matched her version of events. It did not.
Her insurance company continued to deny liability, hoping for a shared liability. It dragged on and on and eventually I insisted that my insurance company serve papers to get the case in front of a judge and let them decide. It was a risky move, but I did not want to back down.
Papers were issued to the 3rd party and they declined to attend court; liability was deemed to be hers and I was refunded all my costs from her insurance company.
I wrote a very bitter letter to that ins. co., telling them I thought their behaviour was disgusting: to persistently refuse to accept liability in the hope of sharing liability for an accident that could be proven to be solely the fault of their insured driving without due care and attention. Also for allowing a relatively simple, inexpensive claim drag out for years.
I sent it registered to the MD and got an extremely weak apology stating that "This is standard practice across the insurance industry and we are by no means unique."
That's OK, then!
Then there's the driver who skidded on ice coming out of a side road and hit me in the OSR.
He gave me an address which my insurance company could not get a response from. As it was local, I went round and knocked on the door. A little old lady answered the door and told me that a family with that name had lived there more than a decade ago.
So, I went to the police station closest to the accident site to report a failure to stop (which it is: even though he stopped, because he gave me false details, it is classed as a failure to stop and provide details).
I had to stand at the desk for over an hour arguing with the civilian on the desk that I had a right to insist the police follow it up; they were trying to tell me they couldn't.
Eventually, they took details and promised to follow it up.
It turned out this guy already had 13 points on his licence (that was confiscated anyway) and a string of other non-motoring related convictions and that is why he gave me false details. Although GMP were not sure why he gave me his real name...
It went to Manchester Crown Court where he failed to appear and was convicted in his absence.
I was able to claim from the MIB (no, not the Men In Black, but the Motor Insurance Bureau) for my uninsured losses, but there was no payment for time off to vist police stations, courts, hassle etcetera...
Sorry to put you through a marathon reading sesh, but the moral of the tale is a positive one: that persistence does usually pay off.