Based on your comments you seem to be drawing too much of a distinction between the words Britannia and Britain, as in fact both mean the same thing. Britannia is just the Latin (and ancient Greek) word for Britain. While there was no Empire of Britannia (or Holy Empire of Britannia for that matter), strictly speaking there was also no British Empire. That is just the informal name for what, at its height, was more accurately called the United Kingdom of Great Britain and Ireland and the various dominions, territories, protectorates and so on that it controlled.
So if you take the historical, but informal British Empire, and alter history by turning it into a real empire with a real Emperor/Empress and give it a more fanciful name by merging the name of historical Holy Roman Empire with the Latin name Britannia and you get what see in Code Geass. The name "Holy Britannian Empire" both invokes the might and culture of the British Empire while also clearly being something else entirely. Similarly, I'd expect any other reference to Britannia as a real country in anime and manga as meant to invoke Britain, but not actually be Britain.
Mind you can't find much evidence that Britannia, as distinct from Britain, being a trope in anime and manga. The two series you mentioned, Code Geass and The Seven Deadly Sins, are the only ones I can find that have a "Britannia". In the later series, it also doesn't appear that Britannia exists as a political entity, just a name for the region where the story is set.
Indeed, I'd say Code Geass is actually an example of the America Takes Over the World trope, as, despite the name, the Holy Britannian Empire is centred in America and doesn't actually control Britain.