Kemi Badenoch might have avoided the cursed 52%-48% ratio which has riven the Conservative party before, but the close-run nature of her 56.5% winning margin in the Tory members’ vote shows the scale of the task before her.

It is hard to overstate the challenges Rishi Sunak’s replacement faces, even setting aside the much-cited fact that the last new UK leader to take a party directly from an election defeat to government was Margaret Thatcher in 1979.

To begin with, as Badenoch acknowledged in her victory speech which came with a warning that Tories must “tell the truth” to win back the trust of the voting public, opposition is just as difficult, especially after so long in government.

There is a sense that quite a number of the 121 remaining Conservative MPs are still only just getting used to the sparse opposition benches and limited number of select committee places, plus the more general sense of chill after the beam of publicity and scrutiny has moved away.

In very practical terms, building her team will be a challenge. There is a limited choice for shadow cabinet posts, let alone the more junior roles. The full Labour government frontbench is 124 strong – more than the total number at Badenoch’s beckoning. Added to that, James Cleverly and Jeremy Hunt have already said they do not want jobs, with some other heavy hitters likely to follow.

Cleverly’s decision leads us to the second and equally tricky problem for Badenoch. When he was surprisingly eliminated from the leadership race in the final round of voting by Tory MPs, it left party members with the choice of two candidates from its populist-leaning hard right.

This was a bitter blow to centrist Tories, with Tory Reform Group, which speaks for many more moderate Conservative MPs, declining to endorse either Badenoch or Robert Jenrick. Some MPs privately said they would not vote for either.

What was perhaps helpful for Badenoch was the way that Jenrick decided to go all-out in supporting the Tory right, pledging to immediately pull out of the European convention on human rights and reduce net migration to more or less zero, while suggesting former colonies should feel grateful to the UK, and leaning heavily into Nigel Farage-style conspiracies over the Southport killings.

As the campaign progressed, Badenoch won the backing of ever more moderate and centrist MPs and other party grandees, some of whom conceded that they were effectively doing so with their noses held, because they believed Jenrick would be so damaging and divisive.

Can Badenoch hold the party together? Based on her political career thus far it might seem that tact, reaching out to disgruntled former opponents and instilling a sense of collegiate unity might not be an obvious strength for someone better known for crossing the road to actively seek a fight. But there is more to Badenoch than this.

Ideologically, she is a mixed bag. Her decision during the leadership election to avoid trying to match Jenrick’s list of highly prescriptive policies, saying the party needed to first reflect and adapt, has paid off. During the one TV debate of the campaign, Badenoch won the respect of an audience of party members by not always giving them the obvious, crowd-pleasing answer.

But at the same time, Badenoch is a sufficiently keen culture warrior to have won the praise of Ron DeSantis, Florida’s book-banning, LGBT community-targeting governor. Her belief that everyone from civil servants to HR departments are the scourge of the UK might seem cranky to some Tory MPs, let alone voters.

Similarly, Badenoch’s temperament could be a work in progress. She is reported to be willing to listen to colleagues who say she must temper a personal style which can veer between highly direct and openly abrasive.

The big question hanging over Badenoch’s leadership is exactly what kind of Tory she’s going to be. Is she, as insisted by her supporters, Keir Starmer’s worst nightmare? Or is she more likely, as some privately believe, to be the political gift that keeps on giving, a never-ending torrent of acrimony and controversy? One thing is for certain, it won’t be boring.