In this list the UK is not listed but the article states: "However, many secular states exhibit tendencies seen in religious states. For instance, the UK is a recognized secular state, but its constitution requires the head of state to swear to protect the Church of England through taking the Coronation Oath."
The list contains several other countries whose head of state is good old Lizzy …

@PontifexMarximus I think you are entirely missing the point...it’ matters not a jot what oath the monarch takes because we are a Parliamentary democracy. The monarch makes no laws...only rubber stamps those made at Westminster by our MPs. The last monarch who tried to usurp Parliament...Charles I ended up without his head in 1649!

@PontifexMarximus Including Canada I believe and Australia ?. The UK does not have a written constitution and the sovereign as head of the Church of England presumably goes back to the split from the Roman Catholic church in the 16th century long before the union of the crowns. The author of the piece is showing his ignorance of the situation in the UK where she is the head of the Church of England only..

@Moravian With all due respect the fact that the UK doesn't have a written document that bears the title CONSTITUTION does not mean that the polity know as the UK or Great Britain and Northern Ireland doesn't have one. Just as the absence of a written document between two parties to a contract doesn't necessarily mean that there is no contract.
Yes QEII is "only" the head of the Church of England but this is a prerequisite for anyone who wants to grab the thrown and the crown. Catholic are explicitly excluded.
Yes Canada, Australia, New Zealand etc. all former colonies that still have Lizzy as their head of state.

@PontifexMarximus I'm not sure what point you are trying to make. Yes the Act of Settlement denies RCs access to the crown. This was also before the union of the crowns so it could be argued that it has no jurisdiction.in Scotland and despite the fact the NI has some of the most vociferous unionists around the province is just a relic of the British Empire and should really be part of. The Republic of Ireland.
The point I was making is that the fact that the queen is head of the church of England has no bearing on whether the UK is a secular stae or not because church and state are totally seperate.and the author makes the common mistake of thinking that England is the UK