Her Majesty picks its Bishops!!!! - hardly a figure head position. As Sovereign Monarch of Great Britain Queen Elizabeth has sovereignty over all within her borders - that includes the Church of England. That is the State Church.
On a separate note: the fracas over Apostolic Succession between the RCs and the Anglicans is a battle that will never be won by either side. Apostolic Succession is properly defined as the tracing of one’s ordination lineage in unbroken succession to the very first ordination at the hands of Jesus Christ. As such, the Anglicans have it.
The Pope (the Bishop of Rome), as a foreign prince (The Vatican is a city state of which the Pope is its head of state. The Vatican sends ambassadors to countries, therefore it is a foreign political power) tried to dictate to the King of England whether he could have an heir to his throne. That is not what I would consider a matter of church business, but rather interference with a Sovereign in the internal administration of his Realm. Don’t forget that the Pope also gave King Henry the title of “Defender of the Faith.” The disagreement over his requested annulment (you call it divorce) is not really the issue over which the Reformation of Roman Catholicism was commenced. But that is for another discussion.
??? He already had an heir to his throne, just not a male one.
And the issue was not whether he could have an heir, but whether he could put away his lawfully married wife and marry another, in clear contradiction of the words of Scripture.