“Kemi is approachable!” Kemi Badenoch, a woman who was, just two months ago, the Secretary Of State Most Likely To Punch You In The Face For Looking At Her Funny was attempting a rebrand. The glasses were gone, and she arrived on stage with a sustained playful giggle. It was disconcerting, like stumbling across Genghis Khan taking part in a pillow fight.

The words had come in a video that showed us what a friendly, calm, not-permanently seething person Badenoch is. It was full of clips of her saying things like: “I love this country because I think it is the most amazing place to be in the world.” You might think this is anodyne, but you’d be wrong: “This is where I think I’m different from someone like Keir Starmer or even Nigel Farage.” You’ll never catch either of them saying they love Britain.

To become leader of the opposition, you need to win the support of the one group of people in the land who think the past 14 years have been a triumph

She had a warning for the Tories that they would need to toughen up. “No more just telling people what they want to hear,” said the only politician in the country with the courage to say that she loves Britain. “If I see something going wrong, I will not shut up, I will stand up and fight,” she added, and that, at least, was completely plausible.

The Conservative leadership campaign has, after a summer of torpor, reached its first moment of crisis. On Tuesday, there will be a closed-door hustings for MPs, and on Wednesday there will be the first elimination round. We’re now in a whirl of attention-seeking. After the Badenoch launch there was the chance to see James Cleverly setting out his stall.

All the candidates have to pull off the same tricky manoeuvre. The Tories’ ultimate route back into power involves a leader of the opposition finding agreement with an electorate that, pretty much, thinks the party has been a disaster in government. But to become leader of the opposition, you need to win the support of the one group of people in the land who think the past 14 years have been a triumph. That’s an exaggeration, of course. Tory members know it hasn’t all been great. But their take on which parts were less than terrific are not those of the country at large. These are people who think True Liz Trussism has never really been tried.

In many ways, Cleverly is well-positioned to appeal to these activists: he didn’t resign from Boris Johnson’s government when everyone else did, he backed Truss and then when she imploded he actually called for Johnson to return. Sadly he ignored a question about what all this says about his judgement.

Badenoch’s explanation for why the Conservatives lost was that they had adopted “a sort of managerialist politics”. We can question whether voters really felt the party was just too competent, but if this really is her diagnosis, her decision to be introduced by Claire Coutinho was particularly baffling. But in this contest, Badenoch is the candidate of ambitious junior officers: Chris Philp, Laura Trott, Alan Mak.

Cleverly, unable to distance himself from a government in which he was both foreign and home secretary, explained that the Conservatives had lost because they had been divided. This, he claimed, was what he’d heard time and again on the doorstep. Without wishing to question his recollection, it does seem possible that the difficulties getting a doctor or a train may have come up once or twice as well.

“I don’t do spin,” she said. “I do do charm. Sometimes.” Somehow it sounded like a threat

Badenoch too seems to suffer from an unreliable memory. Aside from her constant levels of fury, her other exciting character feature is her enthusiasm for making assertions as though nobody in her audience has access to Google. Take, for example, her claim that she “grew up under socialism”. I wouldn’t claim to be an expert on central African politics at the end of the last century, but choice phrases from the Wikipedia entry on Nigeria include “military dictatorship”, “unprecedented total disregard for human rights”, “kleptocrat” and “eight coups”.  It is possible that these are a better explanation of her move to Britain as a teenager than a fear of an over-expansive welfare state.

But a revisionist approach to African politics would emerge on Monday as a surprise theme of the contest. Over at Cleverly’s do, we had got onto Rwanda. You might have though that electoral oblivion was the perfect moment for the Tories to quietly forget that time they sent hundreds of millions of pounds to a murderous dictator in the hope that it would get them a bit of positive coverage in the Mail. That just shows that you’re not leadership material.

Cleverly was very exercised at the “damage” he said had been done to British-African relations by Labour’s decision to abandon a policy that, lest we forget, he privately described as “batshit”. He pledged, marvellously, that a future Cleverly government would revive the scheme. That’ll go over well in Kigali, anyway.

He was, he told us, a “communicator”. Sometimes this can be a disadvantage. Asked how he would achieve his promised cuts to the welfare bill, he rambled at length about over-regulation of childcare. Nobody afterwards was quite sure what he had meant. He had communicated something, but it probably wasn’t the message he intended.

And Badenoch? “I don’t do spin,” she said. “I do do charm. Sometimes.” Somehow it sounded like a threat.