But you don't need access to ANPR for this, particularly.
You just ask the customer to tell you, perhaps with one of those driving monitoring apps/devices that people use to lower premiums. Pretty commonplace now.
FWIW, having worked on car insurance applications, most insurance companies do not much care about microtargeting consumers in this way. Beyond looking at their claims history and the kind of car they are driving, it is a large-scale numbers game, and the way you know which customers, for example, tend to go out more at night when it is dangerous is to look at their age (more likely very young) and gender (more likely male). And then you just make them all pay more. There's no particular reason to get any more forensic than that; it's more costly and it probably doesn't deliver much extra value.
And if young drivers complain, "hey, I am an excellent safe driver, I've done my advanced test, and I don't take risks", you say: "Great. Use one of our driving monitoring apps or devices, prove it and we'll happily give you lower premiums!"
I could tell you a couple of horror stories I am not going to repeat on the internet because they are old news now and times have changed, but I really must say, it's not necessary to imagine what government data could be used for in the hands of insurance companies: it's much more likely that insurance companies will simply incentivise customers to hand over the data. People who want lower premiums will jump through all sorts of hoops to get them.