Is this what Unitatis Redintegratio states? What it does say is the we, Orthodox, are “true Churches” with “apostolic succession” and a “valid Eucharist.”
By having ex opera operato succession, a Christian group is a church. Therefore the orthodox church is given the title church. Why is the Church of England not also considered a church? There is only one reason and Cardinal Ratzinger Head of the CDF (later Pope Benedict XVI) answered this:
“According to Catholic doctrine, these communities do not enjoy apostolic succession in the sacrament of the Orders, and are, therefore, deprived of a constitutive element of the Church. These ecclesial communities which, specifically because of the absence of the sacramental priesthood, have not preserved the genuine and integral substance of the Eucharistic Mystery cannot, according to Catholic doctrine, be called ‘Churches’ in the proper sense."
Had the Church of England not changed changed the rite of ordination and the intentions etc under Queen Elizabeth I they would have also be described as a church by Vatican II.
And the Pope of Rome has authority of the Ecumenical Patriarch of Constantinople or any other Eastern Patriarch for that matter?
Yes, as even Vatican II itself states (which everyone seems to keep mentioning):
“the college or body of bishops has
no authority unless it is understood together with the Roman Pontiff, the successor of Peter as its head. The pope’s power of primacy over
all, both pastors and faithful, remains whole and intact. In virtue of his office, that is as Vicar of Christ and pastor of the
whole Church, the Roman Pontiff has full, supreme and
universal power over the Church… The Roman Pontiff, as the successor of Peter, is the perpetual and visible principle and foundation of unity of both the
bishops and of the faithful.”
LUMEN GENTIUM