Phillip:
What's to stop Henry from simply declaring his church to be autocephalous?
He could do so, but in all likelihood, the Orthodox Churches would not recognize it. If Henry persists, the the Church of England would be expelled from the communion. The end result is probably much like OTL -- a CoE that is neither Catholic nor Orthodox.
I imagine that the rite will continue to be pretty similar to Catholic (or Anglican) practice anyway, so it's not like there will be a period required to draw England out of pagan darkness like there was in Bulgaria.
And what of Russia?
Further, keep in mind that the English were considered heretics by the Orthodox. Until they were brought out of the heresies of the
filioque, Scholasticism, Anselm's PSA, Augustine's Analogy of Being, among others, many Orthodox will see them as no better than pagans.
The churches and priests will already be established.
As far as the Orthodox were concerned, I am not so sure. The bishops in England would, at least, have to be reconsecrated. Further, I am not convinced that many of the English bishops would go along with this -- they would be forced to reject many beliefs that were central to the Catholic faith of the time.
Anyway, this is a pretty silly hair to be splitting. Henry's church will be exactly as autonomous as Henry wants it to be.
That much is true...and returns to my original statement: Orthodoxy will not serve Henry's needs. It will not allow him the autonomy he seeks. It certainly won't reduce the upcoming tensions with the Puritans.
I think the Orthodox Church will be happy to have an Orthodox England, regardless of how exactly the rites or relations with established Orthodox churches are.
History disagrees with you. In particular, consider how the Orthodox responded to the approaches of Melanchton. Consider how the Orthodox rejected the overtures of Rome despite the advances of the Turks. Remember also the dispute between the Eastern and Oriental Orthodox -- few people understand the distinction (if there be one) between the doctrines of the two Churches, but they have remained separated for 1500 years.