Heroines of the Tudor World 

What do you mean by "state church as they had in the East"? If you're talking about Eastern Orthodoxy, we don't have a state Church in the Western sense, as in a single official faith enforced by the government. What we had/still have in some respect is Caesaropapism, meaning the Church takes a back seat to the secular authorities in government. It is not separate from the state, but is an advisor to it, in exchange for protection by the state. The Church is autonomous, not independent, since we never had the religious wars of the West which made full separation necessary. Autonomy will do. This helped us avoid things like the investiture controversy since the order was clear. The Ecumenical Patriarchs of Constantinople never wielded the secular authority Popes had, so the State-Church relationship wasn't competitive. Then in terms of organization we have national Churches, not meant as official state faiths, but as an administrative matter. National Churches tend to be led by a Patriarch who administers an area roughly corresponding to the national territories of states. Do secular authorities have a say in leading and governing the Church like Henry had? No. I can only think of Ivan the Terrible who crossed the line into creating his own... sort of Inquisition and interfering with Church activities.