Anglicanism is the state religion of England, established by law. The church of Scotland (presbyterian) is the state religion of Scotland, also established by law, which the monarch swears to uphold at his/her coronation.
that's what I thought, mike; so the video is wrong in that respect (though I suppose correct in saying that it's a theocracy). The rest sounded fine, though I do not know enough about the Sandwich Islands to be certain.
It is not a theocracy. That term means a country governed by the clergy (e.g. Iran). Having a state religion established by law does not mean that the state is governed by that religion. Most of this is historical, dating back to the 17/18 C when catholicism was feared, not because of its theology, but because it represented continental powers which could seriously compromise the defence and interests of England.
Iran's rulers aren't all clerics (eg Ahmadinejad). Some of Britain's rulers are (bishops in the lords). I think we won't be completely non-theocratic as long as extra support is given to church schools, but I'm not losing a lot of sleep over it.