Not much your GF can do about this, but let her Insurers deal with. The chances are that her Insurers will just pay out to the third party, if they receive a doctors letter confirming possible whiplash. The might query it, if there is no evidence of any damage to the third parties car, but a query is the most it will come to.
It does not make much difference to your GF's Insurance whether the third parties claim is for £200 for damage to their car or £2000 including slight whiplash. The damage has been done, because she had a fault accident and cannot dispute this. ( well apart from saying it was possible the third party had rolled back into her, just to raise doubts about how the accident happened) . If neither your GF or the third party driver obtained the witness details, I doubt that they can be traced. The Police won't look at CCTV, but you could make a subject access request for the CCTV footage, which would cost £10. But such a request, can take up to 40 days for them to action.
Yes your GF's no claim discount will be affected by a fault claim and there will be a loading to the premium as well. She should expect a fairly large increase (30% +) from renewal.
If your GF does not have the third parties contact details, the only ways she could find out is either using the reg no (Ask mid) or via her own Insurers if the third party had been in contact.
There is no point going on about this. Yes it is very annoying and third parties will take the p*ss. 1 in 3 claims now involves a personal injury claim. In some countries, you cannot make a claim for whiplash for such accidents. The UK government is currently looking into this, as it is a factor in the large increase in Insurance premiums.