Did she claim for damage to her own car ?

How much of the increase is down to loss of NCD and how much to a rise in underlying premium? An at fault accident, even with no claim, is likely to lead to your daughter being assessed as a higher risk. Mine went up after a no fault accident where there was100% recovery. Having an accident apparently means you're statistically more likely to have another.

General Accident will (presumably) have a protocol to follow when there is a claim pending. That will include how long it's kept open for and the effect on NCD. Even if the lease company don't claim now it's theoretically possible a structural engineer might discover damage later. And then of course there's the can of worms around possibility that driver or passenger might claim for whiplash - or be induced to do so.

Can your daughter shop around for another provider?

Obviuosly she'd have to declare the accident but another company might take a different view in terms of underlying premium.

If the accident was reported then the NCD may be lost even if no third party has been paid out.

Sounds like GA is being somewhat obstinate, I woud suggest sending a recordered delivery letter to the CE, unfortunately if an insurance renewal is due, you will either have to pay up, or shop arround for another quote

Further illustration of why most people simply don't bother telling their insurers. Perhaps if those insurers would take the time to learn what 'no claim' means and stop shafting people, more drivers would be honest about it like they're supposed to be!