GoodChat · Today 16:28
www.hg.org/legal-articles/who-is-at-fault-in-driving-school-vehicle-accidents-49649
OP there are a few articles on line that are worth reading. It seems that you're the one at fault for the accident and not him, although he can be held accountable for not properly supervising.
I've linked this thread to a friend, who is a driving instructor and he confirms that the learner is in charge of the car and that something spectacularly bad needs to happen, for an instructor to be held responsible.
He has several claims annually, very rarely for a crash resulting from a pupil. Any crash should be used as a learning opportunity. He will stop, try to find the other car owner and assess the damage, taking photos and will get the registration and leave contact details, if the other party can't be found.
He always goes through the insurance and it doesn't go up, like ordinary driving insurance. They expect prangs and it's factored into the cost.
He thinks that your instructor probably wanted to avoid time off the road, having the damage assessed and repairs done, although large driving schools have pool cars, or other instructors will loan, if they're having time off. He will also find it difficult to claim for repairs to his own vehicle, as he hasn't exchanged / left his details, hence the CF wanting you to pay.
Do not pay, he's got you to commit an offence, by leaving the scene. He has insurance to cover damage, but he didn't want the hassle, for whatever reason, so although the crash is your responsibility (it's a minor, everyday thing) he's the author of his own misfortunes.
He may well get points on his licence, if the Police find out and take action. At 6 points, he'll lose his instructor licence permanently.