England's probably your best bet prior to 1066 England had been backing Constantinople politically in the Great Schism, partly I suspect to prevent papal interference in the English church as there were certain aspects of the English church that caused Rome concerns, for instance English priests were still regularly getting married despite Papal injunctions not to. This was part of the reason that the Normans received a papl banner. If William the Bastard lost at Hastings I can certainly see England settling more firmly into the Orthodox camp. This may well influence Scotland and the Irish church too
It's funny that you mention the British Isles because the impetus I had for making this thread was because in my Wales game I've converted several provinces and much of the House of Mathrafal to Orthodoxy due to marriage with Russian nobility. Of course that scenario is anachronistic as heck.