The parents would be convicted for the death's.
Guns are not necessarily illegal in the UK. If you have a valid reason for the gun, then you are good to go. Valid reasons for handguns are rare but shotguns and other hunting weapons are not that difficult to own.
The owner are very responsible for the weapon and will very much serve some prison time if their children get access to weapons and if they are used to kill someone then woe.....
The child responsible will have an interesting time ahead too, in the UK they put children in jail almost as happily as the US.
Any "ops sorry not our fault" defence is not possible, at all. You are strictly responsible for your guns.