It's important to remember that the English Reformation was not a single event, but rather a process spanning several decades and involving a number of different leaders taking the reformation in different directions.
The first major stage was under Henry VIII, usually considered to have begun in earnest with the Statute in Restraint of Appeals (1533) and the First Act of Supremacy (1534). The most prominent feature here was the separation of the English Church from the Pope's authority in favor of Royal supremacy, but there were also some moderate doctrinal shifts and a large push against corruption within the Church. The anti-corruption push in particular was used to justify the dissolution of the monasteries: closing disfunctional monastic establishments and confiscating their assets was already an established practice well before 1533, and the first few waves of Henry's dissolutions were all preceded by "Visitations" (ecclesiastical audits) to find and document abuses and immoral practices that could be used to rationalize the dissolutions. All three major features of the Henrician stage of the Reformation had roots in existing precedents as well as serious ideological supporters. The rejection of the Pope's authority was precedented by the Statute of Praemunire, enacted in 1392 under Richard II, which authorized prosecution against any English subject who used appeals to the Papacy to subvert or undermine Roman authority. Praemunire was somewhat narrower in scope and much narrower in application than the Henrician separation, but served as a long-standing and ongoing precedent for the principle of royal supremacy. Ecclesiastical corruption and revision of theological doctrines were objects of widespread concern, even among people whom in hindsight we think of as die-hard Catholics: people like Sir Thomas Moore (who would later be executed over his opposition to the break with Rome) and Erasmus often had broadly similar concerns over corruption and theology to at least the more conservative of the supporters of the Henrician reformation. Among major supporters of the Henrician reformation, such as the Boleyns and Thomas Cromwell, a frequent motivation for doing so was the belief that the Papacy was too distant and too corrupt to bring about needed reform within England's church, while Henry's break with Rome brought about a golden opportunity for such reform.
There were also figure within the Henrician Reformation, most notably Archbishop Cramner, who crossed the line from reform-mindedness within a broadly Catholic (if not necessarily Roman Catholic) framework into fully embracing Lutheran or Calvinist doctrines. These too had pre-Henrician roots in England. The Lollard movement (*) had its roots in late 14th century England, and in the 1500s it largely merged into the broader mainstream of the Evangelical Reformers who would later be termed Protestants or Puritans. Lollardy was broadly anti-clerical (believing that the church hierarchy was irrevocably corrupt) and iconoclastic (rejecting much iconography and ceremony of Catholicism as vain and idolatrous). In particular, Lollards generally rejected the doctrine of transubstantiation, the Catholic doctrine that spiritual substance (but not the physical "accidents") of the bread and wine of communion were transformed completely into the body and blood of Christ, Lollards generally favored church services focused on sermons and homilies delivered in English rather than song and ceremony performed in Latin, and Lollards strongly favored translating scriptures into English to make them accessible to literate laypeople. The Wycliffe Bible, an English bible translated by an early prominent Lollard, was widely read and owned in early 16th century England even by Catholics despite its association with heresy. In addition, England's urban merchant community had extensive commercial ties to North Germany and the Netherlands, and many Englishmen picked up Lutheran and later Calvinist ideas from them as well as smuggling in a large number Protestant books from Amsterdam printers.
(*) The "movement" label for Lollardy is disputed, as recent scholarship suggests that much more coherence of doctrine and organization among English Lollards was attributed to them by heresy-hunters than actually existed.
After the death of Henry VIII in 1547, the regency for his young son Edward VI (lead first by his uncle Edward Seymour, Duke of Somerset, and later by John Dudley, Duke of Northumberland) fully embraced Protestant doctrines and used the Church of England to promote them. When Edward was dying in 1553, Northumberland arranged for him to disinherit his half-sisters Mary and Elizabeth on grounds of bastardy and instead to will his throne to his cousin Jane Grey (whom Northumberland also arranged to have married to his son, Guildford Dudley, whom Northumberland hoped and expected would rule as king by right of his marriage to Jane). Although the justification for this was couched in legalistic language and concern about the risk of foreign domination if an unmarried woman were to take the throne and marry a Spanish or French prince, one of the main underlying reasons for trying to bypass Mary was her staunch Catholicism. The plan to bypass Mary in favor of Jane lasted about a week and a half after Edward's death before Jane's and Northumberland's support evaporated in the face of the army raised by Mary and her supporters to press her claim to the throne.
Mary adopted an explicit policy of rolling back the Henrician and Edwardian reformations in their entirety, supported by her cousin Cardinal Reginald Pole who was sent as a papal legate to supervise the reconciliation of the English Church to Roman Catholicism. This process proved much more painful than had been expected, for a number of reasons. One was the cost of replacing the church ornamentations and other ceremonial gear that had been gotten rid of under Edward VI. Another was the widespread vested interests among the aristocracy and gentry against the restoration of confiscated monastic lands, which had been widely granted to secular landowners in exchange for money or political support given to Henry or Edward: those who owned formerly-monastic lands, regardless of theological inclination, feared the possibility of confiscation. And perhaps most importantly, the Catholicism that Mary and Pole sought to restore was significantly more rigidly defined than pre-Henrician English Catholism, as in the intervening years Catholicism had significantly redefined itself in opposition to Protestant doctrines. As a result, a great many people who held views that would have been well within the mainstream of reform-minded Catholics in the early 1500s instead found themselves on the edge of being considered heretics by the Marian Restoration. Moreover, Mary's marriage to Philip of Spain proved to be deeply unpopular due to a combination of fear of England becoming a de facto vassal state of the Habsburgs, Philip's personal abrasiveness, and resentment at England getting dragged into Habsburg conflicts with France: incurring steep costs that the cash-strapped English government couldn't really afford, as well as humiliating defeats, most notably the loss of Calais (a major port city on the French side of the Channel coast which had been ruled by England for over 200 years.
One major aspect of the Marian Restoration that helped drive international acceptance of the Church of England among Protestants was the Marian policy of driving opponents of Catholic Reformation into exile in Europe. A great many reform-minded English churchmen and theologians wound up joining Protestant and especially Calvinist communities in the Netherlands and Switzerland, where they helped tie the English Protestantism more closely to the mainstream of European Calvinism.
When Mary died in 1558, she was succeeded by her half-sister Elizabeth. Although Elizabeth had gone through the motions of conforming to the Marian Restoration, after Mary's death she came out as an unrepentant Protestant. However, Elizabeth's protestantism was of a comparatively moderate strain compared to the Calvinist-influenced leaders of the Edwardian reformation, not that far out of line with the Henrician reformers. At this point, what became known as the Elizabethan Religious Settlement was fairly broadly accepted as a tolerable compromise by most of the spectrum of English public opinion when compared to the Edwardian and Marian extremes that had preceded it. Elizabeth's regime was also very careful to frame repression of politically active Catholicism in terms of loyalty to England (prosecuting for treason rather than for heresy), not in theological terms. Crypto-Catholics who practiced in private but were openly loyal to Elizabeth's rule and went through the motions of attending Church of England services were generally tolerated, and even those "recusants" who refused to attend CoE services at least once a year were punished only by financial penalties. The framing of politically-active Catholism as treason was made much easier by the Anglo-Spanish war later in Elizabeth's reign, in which (following Elizabeth's execution of her Catholic cousin Mary Queen of Scots, then imprisoned in England following her overthrow by mostly-Protestant Scottish nobles, for Mary's involvement in an assassination plot against Elizabeth) the Spanish government (lead by Queen Mary of England's widower Philip, who had since inherited the Spanish throne) sought with Papal approval to overthrow Elizabeth and install a Catholic monarch in her place.
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