In practice, the legislative, executive and judiciary powers are separated from the church there too. But formally, yes, that could be a subject of debate.

I'm from Denmark, which like UK has a hereditary head of state as well as an official state church. Neither are really consistent with our democratic ideals, and not something we try to encourage when engaging in state building.

Perhaps we should ask the next Lord Defender of the Faith if he agrees to separations in his church and his state. I wouldn't mind a choicy piece of Wales and Scotland for myselves ;-)