So what I am getting is pretty much any PoD after 1066 wouldn't work due to the sheer cultural differences that were brought in by the Normans, and assimilated in large part by the anglo-saxons. This kinda reinforced the already existing divide between the gaelic/brythonic celts and the germanic anglo-saxons.
My question is how far do we need to go? If this is mostly just a case of political priorities of the aristocracy, with Norman England being too outward-looking, then a surviving saxon state might be better suited for assimilating the disparate polities into a single british identity.
They were certainly more willing to work with different cultures, especially in the aftermath of the danelaw. And we can see that they willing to hire Nordic warrior bands, and even tried to rally their Brythonic populace around a shared Christian identity. They were willing to respect the administrative traditions of the different communities, which went a long way in promoting stability.
Of course all this came at the cost of reduced central authority, if we compare to the continental dukes and kings, but it might just be feasible. Overtime, with gradual conquest and assimilation you might see a Britannic identity emerge as an extension of their common Christian one, perhaps in opposition to the Frankish, German or Nordic attempts to meddle in the affairs of the islands.
I think the easiest way would definitely be to have a post-roman, Arthurian kingdom to somehow conquer and hold the island against armed immigrants, maybe as sort of a high king over the lesser kings of the different tribes.