I can't see how anything other than a change in the law will make a difference. As many have already said, parents cannot control what their young but just-about-adult children do once they are out of the house,
My brother passed his test at 17, and bought himself an old car. He was still in 6th form at that time, but had been working weekends and holidays for many years to earn his own spending money, so it's not as if my parents had any say in the matter, not that I am aware that they were particularly worried about him being on the roads.
He told me recently that (although he was, I think, quite popular already) he never knew he had so many friends until he had the car. Classmates couldn't wait to go out in it with him.
Probably luckily (with hindsight), he had a minor bump in the car not long after he passed his test. I was actually in the car with him when it happen. I like to think that it made him aware of the dangers very early on,
Very sadly though, I too know a family who lost a young adult child in precisely the sort of accident that would not have happened if new, young drivers were not allowed to carry other young passengers, so I can definitely see the reasoning behind calls for a law on that.