I don't know how much the writers of the series stuck to historical fact.
It works from a dramatic perspective to put it on the CoE, and it also
emphasizes the difficulty of being Queen -- you have to please everybody,
and often end up pleasing no one.
The series does discuss the "Divine Right of Kings/Queens" and how the
Crown has been bestowed directly from God. That once she becomes Queen,
she's a representative of God, almighty.
(Highly ironic, since Jesus Christ would have hated this practice. One of
the reasons he was crucified, again according to some religious scholars
and theologians, was because he wanted to overthrow this practice and do
away with Kings and monarchies. King Herod hated him partly because of
this, as did Rome. Which was a militaristic society and monarchy based.
With that in mind, the practice is in a way, anti-Christian. Yet, the CoE
is based in Christianity.)