England could easily be geared towards the domination, cultural and scientific victories, but from a balance point of view it makes sense to pick just 2 of those (England would be overpowered if it had strong bonuses to all three, and useless if it had three weak bonuses all pulling it in different directions). Initially the devs picked domination and culture, which would have been fine -- but archaeology is a ridiculous mechanic to make the driving force behind the English cultural victory. Sure, the British Empire probably got the best ancient loot during the 1790s-1920s "heyday" of archaeology which civ best represents, but that's only because they were in the strongest position to conduct excavations across the globe during that period. The French, the Germans and even the Danes were doing exactly the same thing at the same time, and getting plenty of great loot of their own. The British Museum isn't in the top 5 worldwide in terms of number of visitors; the Louvre is #1.
More to the point, England's cultural prominence has very little to do with its museums. If England's going to be winning a cultural victory, it ought to be through literature (and from the mid-20th century onwards, popular music). Perhaps no other country produced as many internationally renowned writers during the previous millennium, and few countries can rival England's musical output since 1960 in terms of international prominence. Naturally that has a lot to do with English becoming the world's most widely-understood language, but that's exactly the kind of thing that a Civ 6 cultural victory represents: everybody speaks your language. Seriously, though, how many people think of Lord Elgin before they think of Shakespeare, the Rolling Stones or Jane Austen when they think about English culture?
It looks like they're switching England's focus to domination and science in the coming expansion, which is fine by me. A science victory fuelled by iron, coal and engineers makes far more sense for England than a culture victory based on museums.