My entrance into Anglicanism many years ago, while I was a student at Bob Jones University, was through a little Anglican breakaway church called ‘The Anglican Orthodox Church’. The word ‘orthodoxy’ is used by Anglicans not to indicate an affiliation with the churches of the East, but to claim that they are holding to the true historic faith.

David Hall has sent a link to this article by an  Anglican priest posted on the site Virtue Online (strapline: The Voice of Global Orthodox Anglicanism) trying to define ‘Orthodox Anglicanism’ to a Chaldean priest.

The Anglican priest has trouble defining ‘Orthodox Anglicanism’. At the recent GAFCON conference (which was mostly a conference of conservative Evangelical Anglicans) the emphasis was on the Bible and the 39 Articles of Religion. However, this alienates the ‘orthodox’ Anglo Catholics who have no love for the 39 Articles which they regard as unfortunate Protestant propaganda.
Another friend, who is an Anglican minister in one of the many Anglican breakaway churches, explained the difficulty the different breakaway churches have in getting together. “We try to build bridges with the other groups,” he explained “but we have the old prayer book and they use the Roman Missal or they have women priests but we don’t or we have Catholic devotions and doctrine, but they are Protestant and anti-Catholic.”
In other words the definition of ‘Orthodox Anglicanism’ changes depending on which ‘orthodox Anglican’ you’re talking to. For some it is adherence to Scripture and the 39 Articles. For others is is adherence to the 1662  Prayer Book. For others it is adherence to a ‘valid’ episcopacy, the Roman Missal and prayers to Our Lady of Walsingham.
The same problem exists with C.S.Lewis’ famous idea, ‘Mere Christianity’. He called Christians to rally around that core of Christian belief which was the simple faith once delivered to the saints. But what is that core faith? Who defines it? Is it simply adherence to the historic creeds? Does it include the sacraments? Must it include traditional Christian morality? Lewis’ Mere Christianity turns out to be ephemeral. Without a clear definition of what it is, who can say if anyone actually holds to it? The same criticism is made of ‘Orthodox Anglicanism’ and ‘Mere Christianity’ that Cardinal Newman made of the Anglican via media–that it was no more than a ‘good idea.’
There is an additional problem: not only do the various conservative Anglican groups claim that their religion is the true ‘orthodox’ faith, but the Liberals they so despise also claim that they are following the true, historic faith. What conservative Protestants find it so hard to see is that the Liberals also believe they are following the path of true, apostolic, historic Christianity. 
This is how it works: the radical feminists and homosexualists (and whatever other loopy ’cause’) claim that the historic church was always a prophetic church. Jesus was always on the side of the marginalized. He was always standing up for justice. He was always on the side of those who were oppressed by the forces of self righteousness, hide bound tradition, man made religious rules and Pharisaism. The conservatives are those forces at work in the church today. Therefore it is the Liberals who are the truly ‘orthodox’ for they are the ones who bravely stand up against the reactionary forces of oppression, persecution of minorities and religious legalism. The Liberals believe they are the truly spiritually faithful ones, as they hold their heads aloft and endure the persecution (just like Jesus did) of the religious hypocrites.
Once this is thrown into the mix the search for ‘orthodox Anglicanism’ becomes even more complex. 
So just where is the Church? Where is the authority who can define and defend the historic Christian faith? 
As it happens, they have a website: You can find it here.