"My understanding of the structure of the C of E has always been that the Queen is the head of it, but that the Archbishop of Canterbury is the senior ordained clergyman, who runs the show. But if the book says it's both of them, that's the option to go for!
The bank holiday is a really stupid issue, in my opinion - in common usage, we tend to refer to all public holidays as being "bank holidays". But LEGALLY the position is that bank holidays are defined in some obscure Act of Parliament - and there are only four of them - while the other holidays are simply "public holidays". It is absolutely ridiculous for the book to make an issue of the distinction - virtually no-one knows there is a difference, and we all call them bank holidays"
Paul is correct according to 'The Book', but unfortunately you have misread the book yourself. It states that "The C of E or Anglican Church as it is known came into existence in 1534. The King installed himself as head of the Church, and the title of Supreme Governor has been held by the King or Queen ever since"
It also states " The King or Queen has the right to appoint a number of senior church officers, including the Archbishop of Canterbury, who is the head of the Church" (This means that the Queen appoints the A of C) "In practice however, the PM makes this selection on the recommendation of a special committee appointed by the Church"
It is easy to misread the wording in the book, maybe it is designed to confuse you as it certainly does confuse me and I lived here all my life.
Pauls interpretation of Bank Holidays is correct according to the book and I agree with his view that it is ridiculous to make a distinction. There are four Bank Holidays. see page 103 in the book which lists and identifies all the public holidays and distinguishes the Bank Holidays (at least three of them, the fourth presumably being Jan 1st as Bank Holidays are not of nationalistic or religious importance and all the other public hols are just that) from the other public holidays.( the august bank holiday for England and Scotland differ so don't count it twice, each one being at the opposite end of the month)