How is that revisionist? King Harold's family fled to Russia to be reunited to Orthodoxy. Please explain?
Harold vs. William was a dynastic/family dispute, not a church one. Pope Alexander II took William's side in the dispute (partly because Harold supporter Archbishop Stigand of Canterbury once favored a rival claimant to the papacy), but that didn't make Harold a "Greek" (as Eastern Christians were called then by the West). There is no evidence that Harold or any of his allies rejected the Roman Church---that question was settled in England at Whitby (Roman jurisdiction) back in 664 and at Hatfield (filioque) in 680. Harold was crowned by Archbishop Aldred of York, who received the pallium from the Pope. Stigand, who also received the pallium, crowned William after his victory at Hastings.
William, over a period of years, eliminated or exiled his opponents in the Anglo-Saxon nobility, including those in church positions, for political reasons, not religious. Most English prelates had taken Harold's side in the dynastic dispute and were naturally seen as disloyal.
It is true that Harold's illegitimate daughter Gytha was married to Kievan Rus Prince Vladimir Monomakh, but marriages between East and West were not uncommon at that time. In the immediate years after 1054, there was no sense that any schism had occurred. After all, it was mainly a spat between Michael Cerularius and Cardinal Humbert. Vladimir's own sister, Euphraxia, was married to Holy Roman Emperor Henry IV in 1089.
If any of Gytha's kin went with her to Kiev, it would make sense, since they would be in favor there with kin married to the prince. Others went to Sweden, where, of course, they were the kin of the Swedish royals. Others stayed in the British Isles and later warred against William, dying in the effort or going to Ireland.
Sorry for the long-winded response, but the idea that England was somehow not part of the Roman, Western Church before 1066 is a romantic notion with no basis in the historical record. The East and its traditions were just as exotic to English Christians as they were to Christians across the Channel.