Settle privately or through insurance

So myself and ex partner are currently going through a separation where he is moving out this week and whilst we were moving and both driving a car, he drove into the back of me. We were approaching lights and as I was approaching, they turned amber and so if I went though, they would have turned red for him and so he would have ran a red. I know he would have followed vs stopping to wait as he wanted to keep up with me.

Because he thought I was going to go, he has put his foot on the accelerator and so hit me at a bit of speed. It has totally damaged both cars. We have managed to get them to a local garage who will look at them in the next few days but they have said there is a potential both cars could be a write off.

My concerns is both of the cars and their insurance is registered at the same address as that’s where we’ve both been staying, and I’m worried it might look fraudulent to the insurance companies. We would ideally like to resolve this privately so as not to impact either persons insurance but I’m concerned with the cost that we won’t have an option.

Is there any advice or suggestions on what the best next steps are here? They are aware they were at fault and should have 1. Kept more distance 2. Stopped due to light change and 3. Not have sped up to race through the lights.

Thanks