My two cents.
I'm not a Brit, so I don't think I'll ever understand how the British view their royal family.
However, I'm pretty sure it would go something like this.
If the student somehow managed to kill Prince Charles and his wife, you would immediately see the assassin being tackled by both the protestors and the police.
I believe that the British have a certain respect and reverance for their Royal family that goes beyond politics, even with, and almost especially as the Royal family has lost most of it's political power.
The death or killing of a Royal family member is something different entirely from the death or killing of an MP or Prime Minister or something similar. These politicians have political ties, and while not many people would say that just because you're from an opposite part means you shouldn't mourn them, the Royal family isn't political at all. The Royal family simply is, without regard to politics or any of that stuff.
Once the news that Prince Charles and his wife are dead spreads, expect the protesting to die down. In the wake of such an event, I'd expect that Britons would come together in mourning, rather than be torn apart by anger. There may be a few anti-protesters who try to pin the blame on the students, but don't expect them to get much headway.
Expect a compromise on the tuition rates to come about, in a sort of somber, melancholy way. Everybody will be going "Fuck it. Look what all this shit has gotten us." and will be willing to back down from extreme demands.
Expect the assassin to either be lynched at the scene by both protesters and police, conventiently shot while "trying to escape", or something similar.
As I said, I'm not a Briton, so I don't know if any of this is accurate.