Kemi Badenoch is the new Conservative party leader after defeating Robert Jenrick in a members’ vote, becoming the first Black leader of a major UK party and the fourth woman to lead the Tories.

Badenoch took just over 56% of the 95,000 votes, in a poll that had a 73% turnout of eligible members. This amounts to the narrowest win of the four since the party changed its rules to allow party members the final say in contested leadership elections.

Speaking after the announcement in central London, Badenoch, an MP since 2017, who was shadow housing secretary, said the Conservatives needed to face up to hard truths if they wanted to win back the support of voters after July’s catastrophic election result which cut their number of MPs to 121.

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“Our party is critical to the success of our country, but to be heard, we have to be honest,” she said. “Honest about the fact that we made mistakes, honest about the fact that we let standards slip. The time has come to tell the truth.”

She praised Jenrick despite a sometimes bruising campaign, saying: “You and I know that we don’t actually disagree on very much, and I have no doubt that you have a key role to play in our party for many years to come.”

Her words seemed to indicate Badenoch would be happy for her leadership rival to serve in her shadow cabinet, though she will be without James Cleverly, the shadow home secretary, who was eliminated in the final round of voting among Tory MPs, and Hunt, the shadow chancellor. Both have said they want to go to the backbenches.

Badenoch added: “The task that stands before us is tough but simple. Our first responsibility as his majesty’s loyal opposition is to hold this Labour government to account.

“Our second is no less important. It is to prepare, over the course of the next few years, for government to ensure that by the time of the next election, we have not just a clear set of Conservative pledges that appeal to the British people, but a clear plan for how to implement them, a clear plan to change this country by changing the way that government works.”

Victoria Atkins, the shadow health secretary and a prominent supporter of Jenrick, told Sky News that while she was disappointed, “we as a Conservative family really want this to work”.

The prime minister, Keir Starmer, congratulated Badenoch on her victory, saying her achievement in becoming the first Black leader of a party in Westminster was a “proud moment for our country”.

Ed Davey, the Liberal Democrat leader, also sent his congratulations, adding that his party would “continue to offer the best opposition to the government”.

Badenoch, who was born in the UK to Nigerian parents and grew up in Nigeria and the US, was congratulated by David Lammy, the foreign secretary. He tweeted: “Your election as the first Black leader of a Westminster party is an important moment not only for Brits from Black and minority ethnic backgrounds, but for our whole country.”

Another Labour MP, Florence Eshalomi, sent her congratulations “from one British Nigerian MP to another British Nigerian MP”, adding: “Eku ori ire. Your dad would be proud.”

The contest revealed Conservative party membership appears to have fallen by almost a quarter over the past two years with the 95,000 people who voted in this year’s contest a record low.

In 2022, when Liz Truss defeated Rishi Sunak, 141,725 members out of about 172,000 voted. However, by Saturday there were only 131,680 Tory members eligible to vote for the next leader, a drop of 23%.

The contest began in early September with an initial six candidates having secured the required 10 nominations from Tory MPs in order to stand: Priti Patel, Mel Stride, Tom Tugendhat, Cleverly, and Badenoch and Jenrick.

Successive rounds of voting by MPs knocked out Patel and Stride, with the other four remaining in the race for the Conservative conference in early October, given the chance to present their cases direct to party members.

Cleverly was generally seen as having performed best, with Badenoch mainly winning headlines for calling maternity pay “excessive” and suggesting that up to 10% of civil servants were so bad they should be in prison.

In the third round of MP voting shortly afterwards, Tugendhat was removed and Cleverly topped the poll, making him the favourite. But a day later Cleverly was sensationally eliminated himself, seemingly after efforts by his supporters to engineer a runoff with Jenrick and not Badenoch backfired.

The final runoff, in which Tory members chose between Badenoch and Jenrick, involved no head-to-head debates and just one TV event, where the pair were questioned by party members. Jenrick’s camp blamed Badenoch for avoiding debates.