AHC: Have the British isles be incorporated as part of the HRE

As the title says, your challenge is to -with a start date of 1000 A.D- have all of Britannia be incorporated as an integral part of the Holy Roman Empire.
 
Charlemagne conquers Britain and and a successor west Frankish state inherents the title of Holy Roman Empire?
 
I think this is only possible in a TL where west francia is the one that becomes the core of the reconstituted HRE rather that east francia, and thats only a prerequisite.

But with that, its easy to imagine England being incorporated at some point and its ruler given a title like Duke of the Saxon shore.
 
OTL Richard I of England (the Lionheart) was only released from captivity by the Holy Roman Emperor Henry VI when he agreed to 'the surrender of his kingdom to the emperor on condition that he receive it back as a fief' - in addition to a huge ransom (source Encyclopædia Britannica) (wikipedia version is 'King Richard procured his release in exchange for the huge ransom, a further interest payment, and his oath of allegiance to Henry'). On return to England he had himself crowned again as a statement that he was an independent king, not a vassal. Given his character (for example first doing homage to Philip II of France for the English holdings on French soil then later insisting the opposite), I don't think it's too plausible to change this particular incident, but perhaps something similar could happen to another King of England, resulting in that king being recognised as subordinate to the HRE? I find it very implausible that this would continue beyond that individual king's reign though. I also don't see any way of having the whole of Britain in the HRE; that would involve the HRE gaining not just England but also Wales and Scotland. The earlier the PoD, the more difficulties there would be with Viking/Danish/Norse as well; if the PoD is later so that they're not an issue, then the kingdoms are too well established and the focus of the HRE is definitely elsewhere.
 
Top