In a previous life, I was a Defendant Road Traffic Accident solicitor dealing with claims on behalf of an insurer.
A lot of people will try and keep things away from their insurer if they're at fault. However, when the estimate comes in at more than the figure their mate down the pub can get it done at, they usually shy away from paying up.
Easiest option would be to approach his own insurers directly. If he's played ball and notified them, they will have a dedicated third party capture team setup to deal with you directly. They'll arrange for the repair of your vehicle as well as a hire car whilst yours is off the road all at no cost to yourself. It's their priority to keep you happy otherwise you might introduce a third party accident management firm who will ramp up costs with credit hire charges etc etc.
You could go to your own insurer but they will make you pay your excess and you will lose some NCB until they make a full recovery from the third party.