Thank you so much Merlin for the answer you have given here.
I find that the more I delve into this subject of coronation the more complex it becomes.

I am having trouble with the role of the church. I understand how the 'Sovereign is the living embodiment of the State' but do not see why it must follow that the Sovereign 'is inextricably tied to the Church'.

For years now I have understood that the anointing is a sacrament and is just one, important, part of the ceremony. It seems that the entire coronation ceremony cannot be separated from the Church of England, in fact.
But I do feel that a crowning outside a religious ceremony would be OK? Though I'm not sure what it would symbolise.

All the above is my rambling through the mysterious threads of the topic.
I feel sure that many people would say it is just not essential to identify the reign of any monarch with any religious belief.

But with my question I had not intended to get into such deep water over the religious aspects of coronation.
I felt that a coronation might not be essential legally, for a monarch to reign, as for Edward VIII.