Advice please - Truck hit house

Hi

My house is at the end of narrow road, and a truck has ignored the "No Through Road" sign, then attempted to turn around. In the process, he's hit the house. The police were called we were given the incident number.

The damage appears to be superficial but we'd like a stone mason to review and advise what needs done to restore it.

Does anyone have any experience with dealing with companies in instances like this? Ideally, I'd rather not go through my home insurance as I'll lose my no claims and my premiums will increase but will I be forced to do you think?

Or is there a chance the driver's company might want to settle quickly and quietly?

Also, is there any chance of any compensation element do you think? I'm not after a lot but my partner got a real fright and is upset so AIBU to expect a gesture of goodwill as well?

I've been fortunate to never have claimed on any insurance policy so any advice on how best to proceed would be appreciated.