First off, get proper independant legal advice. We can all pontificate to a greater or lesser degree but circumstances like these need a real solicitor, not one who gained their qualifications via a few pints in the bar and friend of a friend heresay.
Having said that, will offer my tuppenceworth as have been requested.... I can only relate to the systems that operates north of the border but no doubt there will be distinct similarities between Scots and English systems which both have Criminal law and Civil law.
This reads like the Criminal case - the Police Involvement - started and finished at the time of the incident and fault was found to be that of the girl, nothing to the driver. The level of proof required at this time would be 'beyond all reasonable doubt'. A fine and/or points can only be determined within a Criminal Court.
The Civil case is now being progressed by the girl. I have been summonsed to the Court of Session (highest civil court in Scotland) on numerous occassions, sometimes upto 6 or 7 years after the date of incident. The level of proof required now, at this stage, is defined by 'the balance of probabilities'. Note the distinct difference. A civil case cannot determine a fine or points on a defendants licence so, unless there is a glaring difference between our two systems, the fine/points thing is at an end.
There will have been a police report of some form made at the time. It should include the names of all who had a bearing on the incident including the Officers concerned, which should also including Trafpol but not always. Force policies vary. If not, those attending should be able to ascertain same from notebooks, call centre logs, shift rotas or simple memory. These people are all witnesses to the case and, by the reading of your scenario, would be classed as on your side as it were.... That report is available to the Insurance company on payment of a small fee.
You pay an insurance premium. That buys a number of things including the potential payout to the girl but not least of which are the services of the insurance companies legal team for cases such as this in order to fight the case and reduce the insurance companies potential payout.
Sadly, a number of insurance companies will pay an out of court settlement rather than involve a team of folks to fight the matter at incredulous daily rates.
I suggest that you get the 'legal team' of the insurance company very much on your side and cause them to get a case prepared. That specifically includes precognosing all those who attended the scene who intimate she ran into the side of your car.
As it reads, your no claims bonus is already on a shaky nail by the very presence of this claim so, in the nicest possible way, you have nothing further to loose by pressing the matter.