Question on traffic islands with marked lanes.

On the edge of our small town is a light controlled traffic island. I was waiting in the outside, right-only lane, in pole position, for my light to change from red, through amber to green. As I started to go forward on the green light, another car came past me on my left to take the next lane to my left which was for going straight ahead. Had he followed the marked course of the lane he was fine. But he took the lazy way of driving in a more or less straight line. To do this he moved a good distance across into my right turn lane and, had I not braked to almost a stop, I would probably have rear-ended his right hand rear corner. Also, because I had to brake, the car following me was very close when he braked, having apparently not seen the action of the car which cut across into my lane.

I am wondering what the insurers would have made of this had there actually been a collision. Good case for having a dashcam?