the Church of England became Protestant in order to become more catholic"
William Van Mildert, Bishop of Durham 1826-36
Van Mildert was a traditional High Churchman, steeped in the theology of the Early Fathers and the Caroline Divines. At first glance his statement looks paradoxical, but what he is getting at is the method of reform. That at the Reformation the Church of England used protestant ideas from the continent to slough off the accumulated abuses of the Middle Ages. Then, interpreting her new formularies in, as Archbishop Parker phrased it, "the most catholic sense" established a national Church which was reformed Catholic in character.
The Anglican Reformation was, in some ways, rather messy, and it owed rather a lot to some of the key players - Elizabeth I, Matthew Parker, and Lord Cecil. They crafted a broadly based Protestant Settlement of Religion that was governed by a conservative revision of the Book of Common Prayer, and from 1563 by the 39 Articles Although the Book of Common Prayer held up very well under pressure, apart from its provisions about vestments being ignored, the Thirty-Nine Articles of Religion (hereafter XXXIX) were soon found to be capable of wide interpretation. The philosophy driving the Elizabethan Settlement was that of making a national Protestant and Episcopal Church. Doctrinally they had tried to comprehend both the Reformed (Calvinist) and Lutheran positions. The result was that the XXXIX largely reflected Lutheran theology except on the topic of Holy Communion where they veered towards the "spiritual presence' views of Cranmer's friend Martin Bucer (1491-1551).
For the first fifty years after 1559, most senior churchmen were High Church Calvinists, and interpreted the XXXIX in that way. They were basically Reformed in theology, but accepted the discipline and liturgy of the Church of England. However, after about 1585 there was a dissenting minority, who, once they became a discernable party, were called Arminians, and later High Churchmen, whose theology was more Patristic in inspiration. They gradually abandoned the Predestinarian theology of the Reformed party, and began preaching the doctrines of Free Wil, Baptismal Regeneration, the Centrality of Holy Communion, and the Divine origin of Episcopacy, all of which they found in the Fathers of the 4th, 5th and 6th centuries. In the later years of James I and in the reign of Charles I they gradually came to be the dominant party in the Church of England, and after the brief Puritan victory of Cromwell's Commonwealth (1644-1660) they were triumphant in the Restoration Church.
The Patristic influenced "Reformed Catholic" theology that they developed and propagated was a dominant school of Anglican thought from the 1660s to the 1840s. From the Caroline Divines, the torch passed to the Non-Jurors, to High Church Whigs like John Potter and Edmund Gibbon, then to the "Orthodox Party" under George III and the Regency, and to E. Harold Browne, and the Wordsworth brothers who were the last major exponants of the tradition. This tradition was absorbed and radicalized by the Tractarians and the Prayer Book Catholics. The older moderate tradition also continued, at least in the UK, and gradually came to be known as Central Churchmanship.