One could read any number of classical works that talk about what it means to be Anglican and find virtually no references to the "See of Canterbury." For example, I’m not sure that the word "Canterbury" appears once in John Jewell’s Apology of the Church of England. If one reads those who articulated the historic understanding of what it means to be Anglican—Thomas Cranmer, John Jewel, Richard Hooker, George Herbert, John Donne, the 39 Articles et al—what one finds is a collection of doctrines and practices: (1) an affirmation of the primacy, sufficiency, and clarity of Scripture, an affirmation of the historic creeds as summarizing the heart of Scripture, an understanding of the church as expressing a kind of continuity with the primitive Catholic Church, and a critique of late Medieval and Tridentine Roman Catholicism as a deviation from patristic Catholicism; (2) certain practices of worship and devotion rooted in Prayer Book worship and the daily office. And, of course, views on the relation between grace and morality, all flowing from and connected to the above. Also, while not a central concern (as it was not a matter of dispute at the time) there are very clear statements about Christian sexual ethics—sometimes in odd contexts, e.g., Jewel’s defending the C of E from accusations of antinominianism, or Hooker’s discussions of why wedding rings are adiaphora but sexual fidelity in marriage is not.
For historical reasons, those who wrote these things were in communion with the see of Canterbury.
But, of course, Anglican doctrines and practices can exist without necessarily being in communion with Canterbury. After 1776, the new American Episcopal Church found it necessary to receive its orders through Scotland. When the Church of South India was formed by the merger of Anglican and Protestant Churches, it was necessary to break communion with Canterbury. And they did so with Canterbury’s blessing.