The Church of England is the established church. This is a formal arrangement, political and cultural. I suspect there is informal establishment as well. Look at the history of the US as a “Christian nation,” and at the idea of “Christendom.” This informal establishment is cultural but not political. I remember the story from my old home town of new president of a major local industry being of a different denomination than the previous president, and all the major executives switching from the old president’s church to the new one.
So I suspect there are two kind of disestablishment, formal and informal. we are seeing the disestablishment of the cultural establishment. I suspect that such a move of executives would not happen today. Church is just not that important any more. The theocons, religious conservatives, are working to undo this, to effect a political ideology of Christian establishment in the political and cultural realms. On the opposite side we hear the idea of the “end of Christendom” greeted with various degrees of welcome, some gleeful and some grudging.
I am not sure where I stand on this. The idea of a Christian culture is pretty tempting. On the other hand, it is unrealistic in the world I can see coming into being.