Neither the Government nor Parliament can tell the Church of England how to conduct its affairs. That separation of Church and Government, though less so of State, to the position of the Church having only a small, apolitical representation in Parliament, has been achieved over the centuries for very good reasons.
The Sovereign is still the Head of the Church of England, but the title is more or less just honorary now and neither can tell the other how to behave.
(Queen Victoria probably caused a lot of mysoginist old male clerics to become very hot under the dog-collar when she used chloroform to ease her labour pains, but they could not really criticise the boss!)
The Church's stance on same-sex marriages is entirely its own business, it has to reflect the general sensitivities of its congregation, and such couples are free to marry elsewhere.
It has to tread a very fine line: if it becomes too modern too rapidly it risks deep schisms. It had enough problems persuading its flocks to accept female priests, with considerable opposition from hard-line Anglicans, especially in countries less tolerant of females and homosexuals than we are in Britain.
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[A couple of years or so ago some para-Christian type on here became very angry with me, eventually blocking me, because I had revealed a friend who had become ordained as a priest, happens to be a woman! Ironically, my critic was also a woman.]
