Ouch! Sorry to hear that.
I’m not an insurance expert but have had to deal with insurance companies more than I’d like over the years both personally and professionally.
My clear understanding throughout is that “without prejudice” simply means no admittance of anything including liability.
I suspect both insurance companies are simply preparing to do a deal between themselves to resolve the matter, and offer a final settlement to the relevant parties to conclude it.
But I watch this thread with interest to see if I am wrong.
Best of luck with the situation.