Kemi Badenoch has the support of her party but the Tories still trail Labour and Reform in opinion polls. By Chris Mason It is Kemi Badenoch's Conservative Party now.

Implicitly and explicitly, that was the message from the Tories' annual conference, which has wrapped up in Birmingham.

It is a party very much united around her, with no murmurings of dissent about her leadership, which is quite the contrast from a year ago.

The pivot point in her time as Conservative leader so far came in her address to this same gathering 12 months back, when, amid constant chatter about the prospect of Robert Jenrick seeking to topple her, she won over the party faithful with an address that oozed confidence. Not just that.

Us reporters were given her speech script, allowing us to follow it line-by-line to help us report what she has said quickly and accurately. But there was a page missing towards the end. On that page was the Conservative crowd pleaser of a plan to scrap stamp duty in England and Northern Ireland.

Fast forward to now and there was a familiar drill. There was plenty of chat throughout the conference and beforehand of a new policy coming on inheritance tax, and, sure enough, another page was missing towards the end of her speech with her plan on that. The plan reopens the fascinating politics and psychology of inheritance tax – which is paid by fewer than one in 20 people but has been described as the country's most unpopular tax.

Why so?

Advocates of cutting or scrapping it say it is because plenty aspire to one day being rich enough to end up having to pay it, plus it is a second tax on already taxed income. But the Conservatives' opponents, even before this speech, were already looking forward to the argument they anticipated after it.

Reform UK, for instance, claim it is a "tax cut for multi-millionaires" and that their plan to cut income tax for millions by raising the threshold at which most people start paying it will benefit far more people.

Policy announcements aside, what stood out in this speech for me was a broader point.

The veteran Conservative elections strategist Sir Lynton Crosby once suggested the party ought to "scrape the barnacles off the boat" as he put it, in reference to unpopular policies that could cause the Tories a headache during an election campaign. This speech felt like Badenoch revelling in pointing at the clean hull of the Conservative ship, what she sees as those barnacles removed, not least the high-profile defections of Jenrick and Suella Braverman.

There was a striking glee and anger in her reflections about Reform UK.

She sought to portray them as sleazy and pointedly decided to lean into an argument of recent months about Englishness. Braverman has argued that, given her Asian heritage, "I'm not English". "I'm proud to be British.

My family and ancestors have a link to Britain which spans centuries. But in no way are we English," she wrote on social media last month, adding: "Englishness is an ethnicity." Badenoch expressed her personal fury at this, saying that as the mother of mixed-race children "I don't want to explain to my son, when we're watching our brilliant England team play football, that some people don't think our black players are English".

The recurring message, today and over the last few days, is Badenoch cannot stand Reform and won't work with them before or after the next general election.

But what she said amounted to an attack on Reform's character and the judgement of their prominent figures, rather than a significant focus on the policies we hear talked about most often by Nigel Farage.

Badenoch did talk about immigration, but not at length. She largely left the issue – and the Conservative policy to withdraw from the European Convention on Human Rights, as Reform also advocates - to her shadow home secretary Chris Philp who spoke before her.

Instead, Badenoch grounded this speech in the big picture tussle to be trusted between Labour and the Conservatives – and in particular who was better placed to deliver a growing economy.

In tone, language and public enthusiasm for the argument, Badenoch and Andy Burnham are quite the contrast with their immediate predecessors Rishi Sunak and Sir Keir Starmer.

Badenoch and Burnham both look like they are enjoying themselves on the stage, and are both enthusiastic purveyors of the core of what are their very different worldviews.

Badenoch acknowledged this with what she called the "battle for the soul of this nation" in the opening minute or so of her address. It is a trailer for the debate to come this autumn and beyond.

The Conservatives feel chipper and are united. But while both of these things are better than the alternative for any party leader, they are not the same as being popular.

And, as Kemi Badenoch acknowledged, they are not there on that score yet, by a long chalk, with opinion polls suggesting they are more unpopular than when they were annihilated at the last general election. The numbers, for them, are dire.

Just not as bad, relatively speaking, as they were.

But they hope things are looking up for them: Reform has had a bruising few months, and Labour, they believe, are leaning to the Left, trying to lure Green and Liberal Democrat supporters towards them.

Can the Conservatives also lure recent Lib Dem supporters in the south of England with talk of help with childcare costs whatever your income, not hiking the council tax of very expensive homes and this inheritance tax plan? This, Tories hope, there are now gaps in the political market they can exploit.

They crave catching and overtaking Reform in the polls, in the hope that after that there is a tipping point allowing them to credibly claim they are the most viable alternative to a Labour or Labour-led future government. Let's see. to keep up with the inner workings of Westminster and beyond.