Insurance for younger family members is a real headache. The premium goes down if they insure it themselves and add a parent as an additional driver - rather than the other way round. Owning a car in a lower insurance bracket (Aygo for example) and fitting a "black box" telematics thingy, all help to reduce premiums. Unless it is absolutely essential to learn to drive (living in the countryside) the advice is to hang ion until after University / 21 years of age before you take your test.
Many youngsters do not have the same drive (pun intended) to pass their test. For me, and many of my contemporaries, it was a burning ambition to pass as soon as possible. In my day it was not considered very romantic to go to the cinema on a bus! How times and attitudes change. We would take every opportunity to get in the car for a drive. Now, when teenagers want a lift, it is a pain!