A modern analogy would be this:
Imagine a backwards country somewhere in the northern European swamps of the doggerland (unsubmerged in this alternative history, just so I can imagine a hypothetical group of people without offending any real population), that didn't have much going on culturally and kinda missed out on all major developments in European history.
Imagine they suddenly become exceptionally good at combat and they are just unstoppable, they conquers all neighbouring territories, they level the Netherlands below the ground etc.
Finally they conquer the British isles, and continue to expand to the rest of europe. The ruling class of the doggerland has always consumed a lot of British culture. They are all well versed in British language and philosophy and media. They do scoff the Brits as weak and decadent by nevertheless they don't have enough of local high culture so the doggerland elite basically turns to the anglosphere for anything that has to do with culture.
Centuries pass. The doggerland empire now is a fixture of Europe. Everybody knows that the origin of the empire is obviously the isle of doggerland and their capital city Doga, the magnificent city.
Nevertheless all doggerland elite travel to London regularly because the cool stuff happens there. The trade network, the culture.
Political figures in doggerland fight for getting appointed as governors of British isles and even if the overseas territories British have colonized in the past because those territories, in the eyes of doggerlanders, are rich and prosperous. They don't care much about other territories they conquered, full of barbarians they don't understand. The Brits are foreign too, but doggerlanders understand them, because they copied them for centuries now.
Centuries pass again and the doggerland empire grants citizenship to more and more of their subject. Most people living in Europe now speak the doggerland language and feel themselves to be doggerlanders. Some of them are indeed settlers from doggerland that have been given land in various parts of Europe, including the British isles. Some of them are locals who have accepted the benefits of assimilating in the doggerland empire.
But Brits didn't feel such a strong push to assimilate and speak doggerlandish. Yes it's the official language of the empire, yes they need to use for legal documents and as a language of the military, but they don't really need to give up to their English since droves of doggerlanders will actually flood London just for the opportunity to learn English. Brits can find employment easily as tutors of wealthy doggerlanders just because they are native speakers of such a prestige language.
Yet the ruling class that rules over British isles is doggerlandish; sure a bit intermarried here and there, but when politics comes into play the pride of being the ruling doggerlanders prevails over the soft cultural games.
More centuries pass. The inertia of the English language is just too big to displace. All doggerlandish elites just speak English. They are brought up with English as their first language and they care less and less of their ancestral language.
Yes they still pay lip service to it, after all they are the descendents of the "great and brave doggerlanders, who conquered the whole known world", so obviously when asked "what people are you?" they will proudly announce "I'm doggerlander, and proud to be one". They may say that in English and nobody would think that's weird. Because in that universe it's perfectly normal for the ruling proud doggerlanders to just speak English. How can that be wrong? They're doing it for generations, for centuries.
Don't tell them they're Brits though! They are not! They are not these weaklings they have been conquered by the valiant doggerlanders! They just speak the language that everybody else speaks because what else should they do?
Now imagine that over time sea levels rise and doggerland gets submerged. The original motherland of the doggerlanders is lost. Their capital now is in London and they speak English and are for many things so different from the doggerlanders that spawned them, but isn't that the case for any society when a millennium passes?