The reason that criminal cases are R Vs Defendant is that the crown (i.e., in practice, the whole of society) is the party taking on the responsibility of prosecuting the defendant. Crimes are dealt with as though the injured party is society as a whole. It wouldn't be fair or reasonable to put the responsibility of prosecuting a crime on to the direct victims, anyway.
And then someone like a member of the judiciary selected to act on behalf of society, and sometimes also a group of individuals acting as a sample of society, are involved in the process of weighing the evidence, deciding on a sentence and all that kind of thing. So it's all about how society was offended against and how society wants to deal with that.
But it means that the sentence isn't "for" the victims, really. It's for society, and whatever society believes the sentence should be for that kind of crime, what the aim of the sentence should be (punishment, rehabilitation, public protection, treatment), what it should be, how severe, etc.
Things have been done round the edges to make victims feel involved, but actually, no, the criminal courts' purpose is not to achieve justice specifically for victims or the families of victims. That might be how the newspapers talk about it, but it's not what "justice" is intended to mean in this context.
There are good reasons why victims or their families aren't and shouldn't be involved in judging and sentencing, such as the fact that many of us (including me, probably) would tend to want far harsher punishments when we've been the victims of something, compared to what society in general might decide makes sense for that crime given the huge range of possible crimes, the available resources for punishment, how to be evenhanded and fair to those who have committed crimes, evidence about how to get the best outcomes, and suchlike.
But a really big reason why you don't want victims to be involved in prosecuting, judging, sentencing, or anything like that, is that having that power would put them in an incredibly vulnerable position. People know they can't easily threaten or intimidate the CPS or a judge or jury, but a victim would have to deal with the possibility of those, or of revenge — as things stand, people know that whatever happened to them in court, the victim(s) weren't to "blame" for it.
I know it sounds callous to say that the justice system isn't and shouldn't be about justice for the families or the victims, but there are good reasons it's the way it is.