“Nate”, recently introduced at the Edinburgh festival, is the thick, swaggering, toxically masculine alter-ego of a brilliant US comedian, Natalie Palamides. Audiences gawped as the diminutive but lavishly male Nate, adorned with a bandana, moustache and scrawled-on chest hair, entered on a motorbike to the sound of Bad to the Bone from Terminator 2, then, to prove prodigious virility, smashed up various props, chopped wood, got his dick (prosthetic, she’s not a magician) out, and persuaded a male audience member to wrestle, bare-chested.

There’s another chance, happily, to see Nate, when Palamides’s show transfers to London, this autumn. Meanwhile, for those who can’t get to the real thing, there’s always – and now more than ever – Boris Johnson.

Shagging, of course. Swaggering, reliably. Sometimes, pictures show, in a bandana. With proofs of masculinity featuring, as well as a broken Foreign Office, the devastation – if Johnson can get his paws on one – of an entire country. If Johnson is not, yet, man enough to live-wrestle, like Palamides, he revealed his affection for this sport, pre marital announcements, in an extended introduction to his latest attack on Theresa May’s Brexit plans. “So it’s ding ding!” he begins, Nateishly. “Seconds out!”

Even the untutored will get the idea: the crisis engulfing Johnson’s career is grave enough to require the activation of completely new and untested combat metaphors, alongside his traditional Second World War repertoire.

“And we begin the final round of that international slug fest, the Brexit negotiations,” Johnson continues. “Out of their corners come Dominic Raab and Michel Barnier, shrugging their shoulders and beating their chests.”

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It’s a while before we return to more familiar Johnsoniana, such as his pre-used “we have gone into battle with the white flag fluttering over our leading tank”; the sort of deranged language that, though it would plainly be regarded as disturbing in any civilian workplace, has been heard so often, from so many, since Brexit’s notables began vociferating in 2016, as to come to sound, in these negotiations, unremarkable.

Not all Brexiters, obviously. It should be stressed that very large numbers of EU-averse individuals, male and female, are capable of discussing the EU without ever mentioning blood, lions or colonies (Farage, Johnson); turds (Johnson); flags (Farage, Johnson); tanks (Johnson); the war/The Great Escape (Johnson, Farage); punishment beatings (Johnson); the “enemy” (Hammond, David Davis’s team); cudgels (Andrew Bridgen); and from Brexit’s more scholarly, Sealed Knot tendency, Napoleon (Johnson, Jacob Rees-Mogg); Agincourt (Rees-Mogg); vassal state (Johnson, Rees-Mogg).

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If nothing else, Rees-Mogg has demonstrated, quite usefully, that quaint diction and a close reading of 1066 and All That are far from incompatible with exhibitions of toxic masculinity, in the commonly understood sense of displays, by covertly insecure men, of extreme bravado, aggression and a disproportionate horror of humiliation (as they call compromise).

As demonstrated by Brexit’s leading sufferers, toxic masculinity’s obsession with winning may be accompanied by leaden declarations of insouciance (Liam Fox, Farage, Davis), by a genuine or affected absence of human feeling (all the above-named), by hypersexualised behaviour (Rees-Mogg’s top hat) and, possibly, by imputations of effeminacy. Johnson refers in his latest attack to the “twanging of leotards” by EU staff, a choice of words that presumably reflects some association, in the great shagger’s mind, between ballet, emasculation and losing – possibly the greatest fear to beset any Nate-minded politician. “Loser” looms large, similarly, in the Trump lexicon.

Did Brexit always have to become, like the current White House, another vehicle for hypermasculine displaying? Certainly, once the debate had been characterised, with the lethal connivance of the BBC (another such platform), as a binary, Westminster-style standoff, as opposed to an exercise in public deliberation, its dominance by bullies, specialists in confrontational flourishes, could have been more often recognised, and deplored. To their credit, Johnson’s “inflammatory” rhetoric was condemned by MEPs. May had rewarded him with a job.

Thus normalised, the language of leading Brexiters has only become more immoderate since the allegedly cerebral Michael Gove began (long before he and Johnson launched their own, more risible hostilities) by comparing (in a Today programme monologue) the UK’s EU membership to the plight of a “hostage”, “locked in the boot of a car”.

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Diminishing hyperbole reserves now leave Today favourite Bernard Jenkin scrabbling, like Johnson, for ever more desperate analogies with which to convey the strange violence of his feelings. Brexit averted, the backbencher writes, “would be like deciding to abandon the Falkland Islands in 1982 without a fight”. M Barnier’s negotiators have plainly evolved, since Fox called them gangsters, into something more closely resembling uniformed Argentinians.

Elsewhere, fellow alarmists talk up the potential for civil unrest with what, given the uneventfulness of Brexit demonstrations thus far, sounds suspiciously like longing. Just what – other than their own predilections – convinces Farage or Barry Gardiner that obstacles to Brexit would risk, respectively, angry riots or “civil disobedience”?

Not least of the many compelling arguments for a people’s vote on a final deal is the chance to see what might happen if the preceding discussion were held in civil or, at least, non-toxically masculine language. How would it be, that debate, minus “slug fests” and “cudgels”, but with the addition of younger voices, of informed ones and in particular of more women, 56% of whom support remain (against 51% of men)? A Loughborough University study found that men enjoyed 85% of the press, and 75% of the television referendum coverage, with starring roles for Gove, Johnson and Farage.

Probably, given the demagogic opportunities, the referendum was always going to be dominated, once they were indulged, by the political world’s most unspeakable Nates. We need to have a new one despite – and ideally without – them.

• Catherine Bennett is an Observer columnist