How does the Anglican Church defend its legitimacy due to the circumstances of its founding?

Introduction

First we need to ask, what should legitimacy be based on? Should it be:

• the approval of the England's parliament?
• Catholic church canon law?
• The will of the majority of the bishops?
• The will of the majority of Christians in England?

Could King Henry VIII make the case that he was accountable to God only, not to the Pope? What if the church was in such a state that there was too much foreign influence (from Rome) that it would be better if the church in England could manage her own affairs under her own King?

Moral legitimacy: corrupt clergy and monasteries

The history books were quite clear that Henry VIII would not have been able to achieve the separation from Rome relatively smoothly (without war) if not for the rise of anticlericalism among the increasingly educated and powerful middle class which started two centuries earlier, when Oxford theologian John Wyclif called for the dissolution of the monasteries due to the worldliness of the clergy, as well as for other reasons.

National legitimacy: rise of nationalism

After the Hundred Years' War "the English people could no longer tolerate the interference into their national affairs of a papacy increasingly regarded as an alien power. .... As early as the 12th century, relations between the English Crown and Rome had been strained, especially where appointments to high clerical office and the competence of ecclesiastical courts in cases involving clergy were concerned."

Political legitimacy: divine right of kings

Henry VIII had probably been influenced by a 1528 book by English Lutheran William Tyndale The Obedience of a Christian Man which argued that a prince was accountable to God only. Another influence was the Collectanea satis copiosa, "a collection of scriptural, historical and patristic texts that was compiled to provide" arguments to justify England's judicial independence and the King's supremacy in Church matters.

Democratic and legal legitimacy: parliament support

In less than two year period, the parliament, which represented a middle class increasingly hostile to Church abuses, wholeheartedly supported Henry VIII with the help of Thomas Cromwell to pass:

• Statue in Restraint of Appeals which is the key legal foundation of the English Reformation by forbidding all appeals to the Pope in Rome on religious or other matters
• Submission of the Clergy Act 1533 to allow the King to legislate on Church affairs
• Appointment of Lutheran theologian Thomas Crammer as Archbishop of Canterbury who annulled Henry's earlier marriage on May 23, 1533
• 1534 Act of Supremacy which declared King Henry VIII and his successors as the Supreme Head of the Church, replacing the pope.

Doctrinal legitimacy: Catholic but without the Pope

Before the breach, when in the early 1520s Luther gained influence in England among several scholars, which included several future bishops such as Hugh Latimer and Thomas Crammer, to implement Wyclif's ideas that the only valid authority was that of Scripture to the point that a small group was nicknamed "Little Germany", the King and the bishops quickly responded by publishing the 1521 The Defense of the Seven Sacraments which earned him the gratitude of the Pope giving him the title "Defender of the Faith".

Although for political reasons the exiled Lutheran reformers were invited back after the 1534 schism, when Henry died in 1547 there was little effect left of the reformation except translation of some parts of the liturgy, prayers, and the Bible into English, as well as minimizing the invocation of saints and worship of relics.

Therefore, at the time of Henry's death the Church of England was still a Catholic church in doctrine except for the leadership of the Pope, although in later decades it would eventually become Protestant.

CONCLUSION

History books showed that preparations were already underway (brokered by Lord Chancellor Thomas Wolsey) to obtain King Henry VIII's desired annulment, but at the last minute, Pope Clement VII prevaricated because of two problems:

• He didn't want to reverse his predecessor's decision (because this will undermine papal authority
• He didn't want to antagonize Catherine's powerful nephew, Emperor Charles V, whom he had to ally with to avoid being imprisoned (!)

Therefore, Henry VIII didn't actually want to breach with Rome, who proved himself to be against the Lutherans about decade before. But he was desperate and there were several factors which benefited England at the time, so he did it with the country's majority support. As shown above, arguments could be made for moral, national, political, legal, democratic, and doctrinal legitimacy.

Resources

• A Short History of the Church of England: From the Reformation to the Present Day by Hervé Picton, 2015, Cambridge Scholars Publishing (sample pages here, which include all material cited in this answer)