In the course of my somewhat idiosyncratic life I have several times been asked that particular question: what I consider being British means. As a child of the British Empire – who grew up, as a Catholic, in places as diverse as East Africa and the Far East – I can only now, in the twilight years of my life, honestly answer the question because my previous answers over decades were – or now seem to me to be – based on some believed in ideology or on some religious faith.
Which recent answer of mine, however unpopular it might currently be, is to refer the questioner to two things.
First, I refer you and them to what a member of the ‘British Establishment’ recently said at a traditional ceremony in Sandhurst:
“In the face of such challenges, Britain’s traditional qualities – fair play, civility, a sense of humour in adversity – remain as precious as they’ve always been.”
Second, I refer you and them to the book Brideshead Revisited, The Sacred & Profane Memories of Captain Charles Ryder by Evelyn Waugh. Or, perhaps more pertinently, to the 1981 television series of the same name starring Jeremy Irons which series for me at least so captures the ethos of that novel and of what being British means and implies.
For there is in those Sandhurst remarks everything quintessentially British – fair play, civility, a sense of humour in adversity – just as in the aforementioned television series there is everything that made the British Empire what it was, despite mistakes and despite the past machinations of selfish, money-obsessed, people; despite the various past ideologies of various politicians, and despite how that Empire history has now apparently been re-interpreted for various political and/or ideological reasons.
For that Britishness – at home, overseas – was, in essence, an embodiment of manners, of a gentlemanly and lady-like way of behaving: a certain standard, and a desire to introduce others to certain cultural values and that standard of personal behaviour. As well as representing our British understated elegance of culture; our tolerant acceptance of diversity and difference; our dislike of displaying emotions in public and often in private; and a certain personal modesty. And of course not only a particular personal equation of dichotomy of belief and way of life sometimes (but not always) solved by the notion of communal duty, but also that interior doubt about (and sometimes a guilt regarding) one’s self born of a feeling that ultimately we are accountable and have obligations to our family, our culture, our faith.
Above all there is – in those Sandhurst remarks, in that novel, and that television series – a presencing of a particular wordless attitude to life such as a reading of Cicero – and an appreciation of the life and loves of Alexander the Great, of the poetry of Sappho, of the New Testament – might, in our reading of their texts in their original language, have disposed us toward. An attitude that even today is sadly not embraced – because perhaps not understood, not empathically felt – by the majority, despite a century and more of State education. Deo Gratias that such an appreciation is still taught in such schools, such places, as still revere what once was termed a ‘classical education’: a learning of Latin and Ancient Greek and hence a reading of texts and authors in their original language.
For one finds in so many classical texts excellent similes of what being ‘British’ (cultured, modest, and possessing the virtue of εὐταξία) means and implies, as in this particular example:
ἐκεῖνός γε μὴν ὑμνῶν οὔποτ ̓ ἔληγεν ὡς τοὺς θεοὺς οἴοιτο οὐδὲν ἧττον ὁσίοις ἔργοις ἢ ἁγνοῖς ἱεροῖς ἥδεσθαι ἀλλὰ μὴν καὶ ὁπότε εὐτυχοίη οὐκ ἀνθρώπων ὑπερεφρόνει ἀλλὰ θεοῖς χάριν ᾔδει καὶ θαρρῶν πλείονα ἔθυεν ἢ ὀκνῶν ηὔχετο εἴθιστο δὲ φοβούμενος μὲν ἱλαρὸς φαίνεσθαι εὐτυχῶν δὲ πρᾷος εἶναι 
The denotatum – British, Athenian, Ciceronian (to name but three)  – may over millennia change but the ethos seems to remain if only (apparently) now remembered and embodied by so few.
Extract from a letter to a friend
 Xenophon, Agesilaus, 11.2
“…this person, whom I praise, never ceased to believe that the gods delight in respectful deeds just as much as in consecrated temples, and, when blessed with success, he was never prideful but rather gave thanks to the gods. He also made more offerings to them when he was confident than supplications when he felt hesitant, and, in appearance, it was his habit to be cheerful when doubtful and mild-mannered when successful.”
 Editorial Note, 2018 ev: As Myatt wrote in a footnote in his book Tu Es Diaboli Ianua, he uses “the term denotatum – from the Latin, denotare – in accord with its general meaning which is to denote or to describe by an expression or a word; to name some-thing; to refer that which is so named or so denoted. Thus understood, and used as an Anglicized term, denotatum is applicable to both singular and plural instances and thus obviates the need to employ the Latin plural denotata.”