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This is honestly a very good question. The US has no official religion, and yet it’s more of a theocracy than the UK in practice. I believe it has more to do with actual practice than anything else. A “pure theocracy” basically says that the monarch is divinely selected. In a way, this used to be the thinking in many parts of the UK, although I don’t believe it has ever been known as a theocracy. The UK now has religious freedom, and as far as I know, there are very few religious laws handed down from the monarchy. So you could argue it’s a theocracy by a literal definition, but not in practice. Being head of the Church of England is primarily a handed-down tradition, with very little power over religion overall.

While the Monarch is the Head of the Church there are 2 things I see that keep it from being a Theocracy,

1.) The religion though a state religion is not imposed as the only allowed religion in the country, as it qould be in a Theocracy. The UK is home to Anglicans, Catholics, Presbyterians, many other forms of Christianity, Jews, Muslims, Hindus, Zoroastrians and many other people and also people whp subscribe to a religion or are Atheist. All are allowed to freely practice and exist without the state penalizing them for not being Anglican.

2.) The role as Head of the Church of England coexists with the role of Monarch and theoretically could be separated or delegated to another individual though this has never happened and most likely never will. It exists seperately as a safeguard against Republicanism, i.e. should the UK become the Republic of England, Scotland, Wales and Northern Ireland and do away with the Monarchy as it did between 1649-1660 with the Commonwealth. The role as Head of the Church of England transferred from Charles I to Charles II despite Charles II living in exile in France and the commonwealth heads were Puritans Oliver Cromwell and then his son Richard Cromwell who inherited ran the country as the "Lord Protector" (which was also a hereditary leadership office) so the office of Head of the Church of England is seperate from the Monarch while simultaneously being held by the Monarch and because the office of that role is separate technically the Monarch isn't acting in the role of Head of the Church of England while doing their job as Monarch. Think of the Head of the Church of England as a form of inherited Papacy or Bishopric where a man or a woman who inherits it. The Pope is actually in the same situation he is both Head of the Catholic Church but also he is the elected King of Vatican the country. So the Pope too a religious head while simultaneously being a monarch.

Church of England doesn't extend to all of the UK I guess.

No Church of Wales but there is a Church of Ireland.

Church of Scotland he is considered an ordinary member.

So I would guess that since he is just the Supreme Governor of a church that extends to a small part of the Nation it could technically fall outside a theocracy?

You could potentially, call England/Great Britain a theocracy in the 16th and 17th centuries when their king or the queen actually held a great deal of political power, but this is no longer the case. Much the same could be applied to Denmark-Norway, and Sweden since they also official state churches that their monarchs were the head of. Currently, however, the monarchs of Denmark, Norway, Sweden, and the UK are all constitutional monarchs and belonging to the official state church is no longer a requirement for full citizenship.

Also, the Commonwealth under Oliver Cromwell could also be classified as theocracy, though Cromwell was not a king.

In a way, it's kind of like a reverse theocracy. Instead of the church telling the state what to do, the state is telling the church what to do.