car accident / incident, just got solicitors letter

they said once there was no collision the other party would never win.

whomever you spoke to in insurance company are wrong - if by your actions you caused the other party to crash (into someone else/wall/whatever) you are liable. I've been through this twice with two motorbike crashes - I crashed both times after taking avoidance action to avoid impact - insurance companies will rule on whether you caused the crash depending on all factors involved (red lights/lane positioning/state of road etc.)

In both of my crashes - first guy jumped onto roundabout and didn't see me already on it and other did illegal right turn across double continuous white lines.
 

Thats possible in some circumstances.

In this case the other party were trying to double overtake on a continuous white line on a poor enough road - its not like they were just driving along doing all the right things.
 
Thats possible in some circumstances.

In this case the other party were trying to double overtake on a continuous white line on a poor enough road - its not like they were just driving along doing all the right things.

This gem of information could change things dramatically. The facts now appear that the other car was overtaking multiple cars on a continuous white line and crashed because of something they caused, not caused by you - if that's true then you should have nothing to worry about and I would let the insurance company sort it out, but it sounds like there is more to this story to have your insurance company offer 50% settlement - ie they believe you were at least 50% to blame.