Well, having posted several quotes from the likes of Archbishop Williams and Bishop Ryle, and having re-read part of MacCulloch's work on Cranmer last night, I may have thought of a new way to look at the question of Anglican identity. It may just be that the answer lies, in part, in who we understand to be the true founders of "Anglicanism". From my own reflection, I think there are at least 3 possible sources for the legitimate Anglican identity.
Firstly, there is the 16th Century Anglicanism of Cranmer, Parker and Hooker. This is the Anglicanism of the Tudors, Henry VIII, Edward VI and Elizabeth I (not so much Mary I, because she had a tendency to burn them). This source is most likely to be termed "Classical Anglicanism", associated as it is with the Book of Common Prayer, the Ordinal and three orders, and the Articles of Religion. And it has been this source that has until recently influenced the direction of Anglicanism most.
Secondly, there is the Anglicanism of the early Stuart period - the Carolinian Church. This is where Archbishop Laud and his descendants in the High Church and Oxford Movements would feel most at home.
And thirdly, there is the Anglicanism influenced not so much by an English theologian or Lord of Cantur, but the Anglicanism imitating Calvin, and even Richard Baxter. Although not mutually exclusive form the first source, if not used well, this third source may ride rough shot of the first source.
There is potentially a fourth source in the various incarnations of liberal protestantism. And although this may claim to large (cashed up) sections of the Anglican Communion, I don't think it can hold a legitimate stake in Anglican identity.
Now all that is left to do is describe the three sources and try and determine which source is bona fide.