This article, from an Anglican blog, is deeply dishonest on several counts. Firstly, in the years after 1054, there were not two denominations, Orthodox and Catholic, in the modern sense. There was a dispute between two patriarchs, but there was absolutely no notion that the entire church had split into two different entities. Except at the Episcopal level, there was still intercommunion, and, in most countries, it remained this way for centuries. Only after the fall of Constantinople and the rejection of the Council of Florence did the Eastern Christians start thinking of themselves as an entirely separate body from the Latin church. Only then was communion broken at the level of laity, and only then do you see Greek Orthodox parishes, under their own bishops, opening in Italy, for instance.
So in the 11th century, it is quite impossible that the Ecumenical Patriarch could have remarked that England was part of 'his church' or that the Pope could have remarked that England was outside 'his church'. There was still only one church, as far as they understood it at the time, and there was no reason that any other nation would immediately pick sides in the dispute between the two primates.
Thus the question of whether England was still Orthodox until the Conquest cannot be a question of canonical reality at the time. It can only be a question of whether the Orthodox Church of nowadays chooses to consider England at that time to have belonged to the true faith. It is purely an opinion, and given the facts-on-the-ground of those years, it is a very reasonable opinion.
The only practical implications of the question would be liturgical commemoration of saints or holy events that happened in England during those 12 years. And it so happens that the appearance of the Virgin in Walsingham occurred in 1061. There is an Orthodox chapel in Walsingham commemorating this apparition. Orthodox worship at the site has been going on continuously for over a hundred years, and pilgrimage groups led by bishops of every Orthodox jurisdiction go there. So it is clear to me that there already exists a liturgical reality that the Orthodox Church considers the Walsingham apparition to be her own, and by extension, that England at the time participated in the True Faith.
This idea, that England was Orthodox for those 12 years, has been around a great many years, and is promoted in a great many corners of Orthodoxy. The suggestions, in this article, that it is an invention of ROCOR, that it is a tool for recruiting converts, that it is a secret belief of the Western Rite - all this is nonsense, and frankly it is libelous to ROCOR.