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.