Any PoD post-1000 where the Anglo Saxons remain in control of England. Basically two questions:
How? and
what happens. Just for the sake of it being a thought experiment (wondering what happens in a TL I might do), what would the short-term effects of an Anglo-Saxon elite enduring in England? And any long-term effects, if we just assume history goes as is for as long as the most liberal interpretations of the butterfly effect be stretched
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And as a side note, I've read the Anglo-Saxons and Byzantines had pretty good relations, is there any chance of them going Orthodox or anything wack like that?
Well, the effect is going to depend in great part on the specific choice of POD. As for possible PODs...
1) The obvious one...Harold Godwinson beats (and preferably kills) William the Bastard at Hastings.
2) Another, less obvious one...Edward the Exile lives long enough to succeed Edward the Confessor when he dies in 1066, and rules for about a decade afterward, giving Edgar the Atheling the chance to mature and succeed to the kingship when Edward the Exile dies (say in 1075-1080). The succession passes lawfully from one King to another, and the Normans never get a foothold in England.
3) An even earlier one. Edmund Ironside (don't you just love Anglo-Saxon nicknames?) defeats and kills Canute at the Battle of Ashingdon on October 18, 1016 and re-establishes the hold of the House of Wessex on the crown. He lives to the age of 60, surviving until 1048, when he is succeeded by his son, Edward (Edward the Exile in OTL). In this ATL Edward probably marries an Anglo-Saxon lady, rather than a Russian or Hungarian (the origins of his OTL are uncertain), and the OTL Edgar the Atheling is never born. Instead, another prince born of Edward and his ATL wife is born and inherits when Edward dies, lets say, for fun, in 1066. Once again, the Normans never get a foothold in England.
4) An even earlier one...Aethelred the Unready never marries Emma of Normandy. The Normans do not get a dynastic connection which gives them a claim, however tenuous, on the English throne. There is no Edward the Confessor. Couple this with a POD where one of King Aethelred's six sons by his first wife survives to inherit after the death of Canute, and you most likely have a surviving Anglo-Saxon England.
All of these will have different effects.
--A POD that involves the defeat of Canute by Edmund Ironside, while preserving the marriage between Aethelred the Unready and Emma of Normandy, will likely lead to an England which is somewhat oriented toward France due to the Norman bloodline within the Anglo-Saxon royal family.
--A POD where Edmund defeats Canute, but the marriage between Aethelred and Emma never took place, might see Anglo-Saxon England not orienting itself to either Scandinavia or France, but trying to proudly maintain it's own traditions.
--A POD based on the victory of Harold Godwinson at Hastings likely leads to an England oriented toward Scandinavia and away from France. The Godwinsons were partially of Scandinavian heritage, and Harold and his successors would likely reject France and French influence because of French support for the Normans.
--A POD based on the survival of Edward the Exile might still see conflict with Normandy, but with stronger internal support for the Anglo-Saxon monarchy due to the succession being seen as more legitimate (there were many who viewed Harold Godwinson, with good reason, as a usurper).
So you see, it's really all a function of which POD you pick. And there are many more to choose from. The above is just a quick list of the more obvious ones.