The history of the British Isles is complex, lengthy and very difficult to fully understand. It is also old, so that all "facts" are open to interpretation.
There is disagreement of varying amounts with almost every fact from before 1900, and certainly any interpretation.
Having said that, "English" was a term coined in about the 5th Century to encompass the amalgamation of the Germanic tribes and the Brytons.
Here is where the real problem develops. Although the Welsh, and the Scottish, like to use the term Celtic to describe themselves, the term "Brytons" seems to have specifically referred the the portion of the Celtic people that lived in Great Britain (the island), ie not the English, or the Normans.
The Brytons great contribution to the culture, leadership and population led to the term British, later (eary medieval) coming to mean all the residents of the island, including the English. Being offended by being called British is a bit barmy IMHO, as the name actually derived from them, but oh well, that's history for you.
In the game, we have the Celts (which should include the Brytons). The English should include the Brytons. And as soon as they use British it is a bit of a mess.
'Britain' is first recorded as 'Bretannikē', or so Strabo tells us, in the works of Pytheas of Massalia (4th century BC, now lost), who had reportedly travelled extensively in the northern seas and islands. Etymologists speculate that the word is derived from a root 'Pretania' or 'Pritannia', a cognate of Welsh 'Ynys Prydein' (the island of Britain) or Irish 'Cruithen-tuath' (land of the Picts). Irish/Scots root 'cruth' and Welsh 'pryd' gives us 'form', so the British are 'people of forms', ie., tattoos. Cf. Latin 'Picti', painted, ie., tattooed.
The middle ages witnessed a great deal of interest in a romanticised 'British' past with Geoffrey of Monmouth playing a leading role, and the Arthurian romances are its most widespread and lasting legacy. Henry Tudor sought to play upon his Welsh background by invoking the 'British' romance tradition repeatedly, notably in naming his first-born son Arthur. The conceit dwindled under his successors, although the various legal jurisdictions of Wales were brought under the English Parliament in the Laws in Wales acts between 1536 and 1542. The claim that 'this realm of England is an empire' predates these, coming in the 1533 Act in Restraint of Appeals (ie. to Rome), and should be seen as one more in a long line of claims by English kings to sovereign authority dependent on no outside power, whether pope, emperor, or other king.
'Britain' heaves back into view in the writings and speeches of James VI and I and his courtiers, who found it a powerful image to invoke in speaking of his dual monarchy covering the entire island. Talk of a 'British Empire' to describe the composite monarchy and its colonial possessions began in the seventeenth century, analagously to the use of the 'Spanish Empire' as a shorthand for the patchwork of kingdoms and principalities in the hands of the kings of Castile, Aragon, etc.
After the Act of Union in 1707, the term 'Great Britain' referred to the state as well as the island, although the English habit, endlessly irritating to their neighbours, of using 'England and Britain' interchangeably appears well-established within a few decades. This interchangeable use, it is worth noting, has long been common in French, German, Spanish and Italian, and also in America. One constituency for whom the term Briton did carry emotional and political appeal through the eighteenth century were Scottish defenders of the Union. David Hume refers more than once to himself as a 'North Briton', though the name later became associated more with the cause of the radical John Wilkes.
It is worth noting that Ireland has never been subsumed within the term Britain, the Act of Union of 1800 created the United Kingdom of Great Britain and Ireland; the independence of Eire in 1922 leaving the United Kingdom of Great Britain and Northern Ireland. And a final note, the 'Great' in Great Britain is a geographical term, differentiating the largest of the British Isles from the peninsula of Brittany, settled by Britonic speakers in late antiquity. It is clearer in French: 'Bretagne' and Grande Bretagne'. Interestingly French, following Latin, retains the Feminine form first given the noun by Pytheas.
And yes, I am procrastinating.
