“This isn’t a TV reality contest!” So declared defence minister Tobias Ellwood, when asked by Sky News’ Sophy Ridge about the forthcoming Conservative leadership race. To which there is only one honest response: that’s precisely what it is. Even as the new Brexit deadline draws closer, the Labour-Tory talks collapse, the Commons prepares to reject Theresa May’s withdrawal agreement for the fourth time, and the Conservatives face disaster in Thursday’s European elections, senior contenders for the top job merrily parade themselves, their spouses, and their kitchens in a grotesque bid for support in a contest that has not yet officially begun.

They can’t run the country, pass the legislation it needs, or arrange its departure from the European Union. But they’ll do a mean photoshoot for you at the drop of a hat. To govern is indeed to choose.

The instinct to hang on is etched into May’s DNA and she has still not given her party a resignation timetable. But the electoral kicking that the Tories face this week at the hands of Nigel Farage’s Brexit party will loosen her long-failing grip – and the rejection of the withdrawal agreement bill next month must surely force her to confront the question with greater clarity.

She still yearns to be remembered as the prime minister who implemented the 2016 referendum result and took Britain out of the EU. Failing that, her party is offering her the consolation prize of miming the nation’s exit by her own speedy departure from Downing Street.

Whatever the precise date of that inglorious occasion, the world’s most horrible beauty contest is already up and running. Tomorrow, the One Nation group – including cabinet ministers such as Amber Rudd, Rory Stewart and Greg Clark – is relaunching itself in an explicit bid to contain the rise of rightwing nativism in the party.

I wish them well. But, as they well know, they face an uphill struggle. The modernising spirit of the early David Cameron years is now a distant memory. The virus of Brexit has spread in the Tory bloodstream and toxified its politics: what was once the party of economic competence has transformed itself into a cultural movement. Whatever the government’s press releases say to the contrary, it cares more about immigration than it does about prosperity. Which is why Boris Johnson is runaway favourite to be the next prime minister.

Former Brexit secretary Dominic Raab. Photograph: Adrian Dennis/AFP/Getty Images

To those fortunate enough to be unversed in Tory politics, this prospect may seem inexplicable. Why, in 2019, would the party pick as its fresh start one of the architects of the globally scorned disaster that is Brexit; a politician who, as foreign secretary, demeaned a great office of state; a polemicist who thinks it is acceptable to say that a Muslim woman wearing a burqa resembles “a bank robber”, and that it is “absolutely ridiculous that people should choose to go around looking like letterboxes”?

It’s a fair question. Plenty of Tory MPs – probably a majority – find the idea of Johnson as their leader appalling. But it does not follow, by any means, that they will exclude him from the final pair of candidates who go forward to a vote by the Tory rank-and-file.

First, they would not dare: according to a YouGov poll of Tory members in Saturday’s Times, Johnson is 26 points ahead of the next most-popular candidate, Dominic Raab, another populist Brexiteer.

Second, many Tory MPs are now approaching the next general election as an exercise in damage limitation – or, to put it more plainly, saving their own seats. According to a Politico-Hanbury survey published this weekend, Johnson is the only candidate who presently stands a chance of preserving the existing Tory electoral coalition (a demographic combination, please remember, that failed to deliver the party a majority in 2017). One hears the arguments already around Westminster: yes, he’s terrible; yes, he’ll put some people off; but he’ll see us through the storm until we find someone from the next generation to replace him.

But this is epic self-delusion. Johnson’s name recognition is certainly remarkable, and reflects his former persona as a chatshow favourite and Wodehouse-quoting English eccentric. But the “Heineken Conservative” – who reaches the voters other Tories cannot reach – is long gone. That vanished when Johnson took the plunge in February 2016 and (having written pieces supporting both leave and remain) opted for Brexit. Since then, he has been an intrinsically divisive figure, a rightwing populist who still occasionally lays claim to the One Nation tradition – but without the slightest credibility.

The election of Iain Duncan Smith as Conservative leader in 2001 taught me that predicting the outcome of such contests is a mug’s game. But the odds, at least, stand firmly in Johnson’s favour.

What is certain is that he would be a terrible leader: distracted, hubristic, persuaded by his own mythology. He would nurture Conservative tribalism, and encourage precisely the magical thinking that his party urgently needs to escape. In what is likely to be a short premiership, he would slam the door shut on the Tory echo chamber and – from within – bellow that great things can be accomplished by force of will and charisma alone.

After the briefest of honeymoons (public curiosity about a new prime minister is powerful but generally short-lived), the voters would quickly start to wonder how this spectacularly incompetent braggart, with a Churchill complex but no Commons majority, had ended up in Downing Street in the first place.

Cue a general election, in which absolutely anything could happen. If I were Jeremy Corbyn, I know who I’d be longing for as my next opponent.

• Matthew d’Ancona is a Guardian columnist