England is to Britannia as Castille is to Hispania.
Hispania was the Roman name for the Iberian peninsula and the term "Hispani" included all ethnic groups from the Iberians of the south, to the Celt-Iberians of central Hispania, to the Celts of Galicia in the northwest to the Basques. The Castillians did not exist as a people during the Roman times and, when they later formed as a unique society, included people descended from barbarian invasions.
Likewise, Britannia was the Roman name for the British Isles and the term "Britanni" (Britons) would have included the inhabitants of what is now Wales as well as what is now England. "Englishmen", like the Castillians, did not exist as a unique people during the Roman times and, when they later formed as a unique society, included people descended from barbarian invasions.
Great Britain is populated by English, Welsh, and Scots. Only the Royal Family is "British."
Go, Trojans! Beat the Hawkeyes!