The queen is nothing more than a figurehead when it comes to church affairs. Its a historial accident that she is the head of the church of england.
The church of england structure of government is similar to the catholic church in that we have bishops and archbishops.
"Anglican Communion
Further information: Anglican Communion § Provinces
Member churches of the Anglican Communion are often referred to as provinces. Some provinces are coterminous with the boundaries of political states, some include multiple nations while others include only parts of a nation. Some, such as the Church of the Province of West Africa, have the word "province" in their names. These member churches are known as "provinces of the Anglican Communion," and are headed by a primate, who may also be referred to as a primus (for example, the Primus of the Scottish Episcopal Church), presiding bishop, or moderator.
The word "province" is also used to refer to groupings of dioceses within a member church. The Church of England is divided into two provinces: Canterbury and York. The Anglican Church of Australia has five provinces: New South Wales, Queensland, South Australia, Victoria and Western Australia, and an extraprovincial diocese. The Anglican Church of Canada has four: British Columbia and Yukon, Canada, Ontario, and Rupert's Land. The Church of Ireland has two: Armagh and Dublin. The Episcopal Church in the United States of America numbers, rather than names, its nine provinces."
en.wikipedia.org/wiki/Ecclesiastical_province
The church of england in different parts of the world are already allowed a lot of freedom.
This link is from the church of england website. Look at page 13.
www.churchofengland.org/media/38963/gsmisc910.pdf
The church of england is a world wide group of mostly english speaking (protestant) christians. There is a lot of diversity of belief.