We got the information about the car via Parkers website.
Trying to report the incident was an interesting experience. I googled 'how to report dangerous driving UK' and found advice (dated 2016) to tell DVLA. DVLA has only one phone number, and after pressing buttons, and holding, I finally got through to a live person - who told me I must tell the police on 101.
I rang 101, and got through to the automated answering service of my local force.
Tried again, selecting the option for a different force - we were miles away from home when we saw this daft girl - and finally got through to a member of the relevant police force. He took the car number, and told me that if the car is not taxed it will eventually be picked up (CaroDane, you were right) but that they can do nothing unless I go to a police station to report the incident. I am not going to do that. It would take half a day, given where I live.
I can't help wondering what the reaction would have been if we had videoed her and posted it on the internet?