The Church of England's own account and the historical account diverge here more sharply than in most traditions, and both are defensible.
The historical occasion is not in dispute. Henry VIII wanted his marriage to Catherine of Aragon annulled, Rome would not oblige, and the Act of Supremacy of 1534 made the king supreme head of the church in England. Henry was not a Protestant and did not become one; he dissolved the monasteries, took their wealth, and burned both Lutherans and papists. The actual doctrinal reformation came under his son Edward VI, in Thomas Cranmer's prayer books of 1549 and 1552, was reversed under Mary, and was settled under Elizabeth I.
The church's own account is that it did not begin in 1534 at all. On this reading there was a church in England before there was a pope with jurisdiction over it, the sixteenth-century acts removed a foreign usurpation rather than founded a new body, and the continuity of bishops, parishes and buildings across the break is the proof. That claim is why Anglicans call themselves catholic and reformed rather than simply Protestant, and it is not merely rhetorical: the medieval structure really did survive largely intact.
The Elizabethan Settlement is the tradition's characteristic move. Rather than resolve the disputes, it produced formularies deliberately capable of more than one reading, the words of administration at communion combine a Catholic and a memorialist sentence, and required conformity in worship while leaving belief comparatively unpoliced. Whether that is wisdom or evasion has been argued inside Anglicanism ever since, and the argument is currently being conducted by other means.