I personally don't think we need a POD as far back as 1066 to achieve this. All what we need is an England which during the age of nationalism espouses a staunchly 'Anglo-Saxon' nationalist variety that solidly looks back to Anglo-Saxon England pre-1066. This ATL nationalism would be largely based on OTL thought, such as that of the 'Norman Yoke' and the Whiggish interpretation of history, which stated that Anglo-Saxon England was a kind of Garden-of-Eden liberal constitutional monarchy in which the Witangemot was England's first parliament, and that the Normans destroyed all that by imposing a foreign autocracy.
So what we need is an ATL English nationalism that emerges, say, in the long eighteenth century after the revolution of 1688 that is a reaction against French-backed Catholicism and Absolute Monarchy and could see Dutch support for that revolution and William of Orange as a sign of pan-Germanic (and Protestant) solidarity. This Anglo-Saxon revival, for it to permanently confirm England's place in the 'Germanic Club' would have to last continuously during the Eighteenth and Nineteenth Centuries. In addition to changing/ requiring a change of England's self image, literature and politics, I imagine that the following changes would be noticeable:
- The mass re-adoption of Anglo-Saxon first names in England during such a period: Names such as William, Henry and George go into decline and normal English names become names like: Athelstan, Edgar, Elfgar for boys and Godgifu, Elfgifu for girls. Scandinavian names (very popular just before 1066) could also become the English norm, such as Sveyn and Bjorn, which would further 're-scandinavianise' England.
- Indigenous English roots being used for new words that enter the language rather than importing Greek and Latin for say, modern concepts and technologies.
- The use of Anglo-Saxon words for newly created political institutions - so that when, for example, the American Revolutionaries were creating their constitution, instead of using the word Senate, they use the Anglo-Saxon word 'Witan' to refer to their upper house. Likewise when County Councils are created in England in 1889, have them be called 'Shire Moots' instead.
If this Anglo-Saxon revival is as thorough and central enough to England's identity, then the two world wars, although shattering pan-Germanicism, would not be enough to undoe England's Germanic Identity, any more than it has made the Netherlands less Dutch post 1945.
But this TL would be quite interesting. It would mean that English/British nationalism would be pan-Germanic in nature and not Anti-continent, as in OTL.
A striking WI question would be how would such an English nationalism effect the other peoples of the British Isles. In OTL, German romantic nationalism in the Nineteenth Century was a key factor in inspiring the other nationalities of Central Europe and beyond to start asserting their own identities. If, in this TL, England asserts her Anglo-Saxonness, then I could easily see the Welsh asserting their Celtic-ness. In this TL, Wales would be more like Ireland and develop a nationalist movement of her own, which in OTL didn't really happen until the 1920s.
If this is the case, then I can see a Welsh TL where, in England, the OTL 18th Century Druid-mania is replaced with Anglo-Saxon Nationalism, and so the Druid movement, instead is largely Wales-only, and rather than being pan-British, becomes Welsh Nationalist by the 19th century. This is going off on a tangent, but in this ATL, the Chartist uprisings in South East Wales in the 1830s and 40s are, instead Welsh-nationalist uprisings like the 1798 one in Ireland, and their subsequent repression by the authorities and backlash against the Welsh Language (like the Austrian suppression of Hungarian post-1848) makes Wales and the Welsh public staunchly Welsh Nationalist by the Second Half of the Nineteenth Century, with a Home Rule movement dominating politics in the country.
So, this TL makes England more Germanic and Wales more Celtic.