> What actually matters is that those breaking the constitution, be it written or not, can be held criminally liable. Can you be held criminally liable for breaking "a set of customs and principles" in the UK?

Not exactly. If there's enforcement, it will be done by other actors in the system will cooperate to enforce those "customs and principles." There's no appealing to some higher authority for enforcement (and especially not criminal law, which would be a lower authority).