Labour is claiming that The Right Way, the mini-book published by this week setting out her political philosophy, shows that the Tories are not committed to the minimum wage.

In the book, Badenoch says:

Britain took the wrong way in the late 1990s when Labour governments came to believe that prosperity could be mandated by ministers. If wages were too low, ministers could mandate them higher and if investment was insufficient, they could direct savings.

The Tories have supported the minimum wage since it was introduced by Tony Blair's government. But, commenting on Badenoch's words, , the Labour chair, said they showed that at heart the Tories do not support the idea.

It's the same old Tories. They never learn. The Conservatives opposed the minimum wage when Labour introduced it, and they're still opposed to it now.

Kemi Badenoch is the latest in a long line of failed Tory leaders who are determined to see workers made worse off. When so many people across Britain are struggling with the cost of living, it's about as tin eared as you can get.

Kemi Badenoch needs to explain why she is so unhappy that workers were paid a minimum of £3.60 per hour – or does she think they should be paid less than that now?

Reform UK will use an open primary to choose a candidate to take on Kemi Badenoch in her North West Essex constituency, the Telegraph is reporting.

At the last election Badenoch had a majority of just 2,610 over Labour. Reform UK was in third place. But the party does well in Essex, and Nigel Farage has claimed it could beat Badenoch in her own seat.

In his Telegraph story, says:

The local [Reform UK] branch will choose the three finalists, with the final choice put to everyone in the constituency who wants to vote after a special hustings chaired by Mr Farage.

It would echo the open primaries held in a number of US states, which allow residents to vote for their favourite Democrat and Republican candidates even if they are not registered as party members.

Normally parties just let local members select local candidates. Open primaries in theory allow them to choose candidates who might have a wider appeal to voters who have previously supported other parties.

David Cameron experimented with open primaries before the 2010 election. In two seats – Totnes and Gosport – the party sent ballot papers to every voter in the constituency giving them the chance to help pick the Tory candidate. In other seats, anyone who attended an open meeting was allowed to take part in the selection vote.

But the Tories did not repeat the experiment in later electons. The candidate selected for Totnes, Sarah Wollaston, turned out to be quite independent-minded, and she eventually left the Tories, first for Change UK and then the Liberal Democrats.

This is what the City of Sanctuary organisation has said in response to Laura Trott attacking its Schools of Sanctuary network. (See 1.13pm.) A spokesperson said:

For many children, the experience of forced migration isn't an abstract debate - it's their own story, or the story of a friend sitting next to them in the classroom. Schools of Sanctuary supports schools to make sure these children, and all children, feel welcome, understood and able to thrive.

We help teachers understand what children may have been through and give schools practical ways to make sure every child feels they belong. We're incredibly proud of the schools doing this work every day, often in very challenging circumstances. At a time when division and hostility are increasingly part of public debate, this work matters more than ever.

We are a registered charity and therefore non-partisan, and fully comply with Charity Commission guidance on campaigning and political activities.

, the shadow education secretary, may have been speaking to a minuscule audience in the hall earlier (see 11.18am), but she gave a long speech that covered quite a lot of ground. Here are the main points.

Today I'm launching Our Pledge to Parents which lays out my commitment to mums and dads. I will keep political activism out of the classroom.

And she singled out teaching unions for particular criticism.

We'll properly enforce the rules on political impartiality for teachers and guest speakers.

And we'll create a specific law around trade unions involved in education.

They must not bring politics into schools.

Children as young as seven are being told they have white privilege.

Pupils are learning that a woman can have a penis, a man can be pregnant, and sex is assigned at birth.

Some have been told to rewrite negative headlines on migration to make them more positive.

And others have been taught that Britain is a racist country.

This is fiction being presented as fact ….

This is part of a trend of complex, controversial, contested issues being boiled down, laced with political bias and delivered in a place that children trust; schools.

If anyone has an agenda, it's a network called Schools of Sanctuary.

Now you might not have heard of it, but it has now signed up over a thousand sixth forms, secondary schools, primary schools, even nurseries,

All calling themselves schools of sanctuaries for refugees.

The vision schools are signing up to is that the UK will be a place of welcome for all.

Except it's more nuanced than that isn't it?

We can't welcome all migrants.

We don't want to welcome all migrants, certainly not dangerous criminals.

Yet that is the simplistic political narrative they push on our children.

But when I wrote to the former education secretary [Bridget Phillipson] about this blatant political activism, do you know what she did?

Absolutely nothing.

• She also condemned the role played by the National Education Union, England's largest teaching union, in schools.

What do you think they debate when the NEU, that's the National Education Union, get together?

The merits of teaching Latin perhaps?

The value of coding in maths?

The latest developments in pedagogy?

No.

Their recent resolutions include:

Defending the right to protest, opposing UK defence spending and embedding their own LGBT+ teaching materials in schools.

Friends, this doesn't sound like a professional body that cares about teaching pupils.

It sounds like a campaigning organisation bent on politicising education.

And it is deeply entwined with politics, extreme politics.

Several NEU officials happen to also be directors of the Palestine Solidarity Campaign.

Parents … are being left with an impossible choice.

Sending their children to mainstream schools where Jewish children are heckled, bullied, singled out, or send them to Jewish schools, with prison-like securitywhere they're under constant threat from outside.

You might have heard about the school in Barnet making the hijab part of the uniform for girls as young as 7.

Conference, be absolutely clear, we would not allow that under a future Conservative government.

Lucy Powell [the education secretary] says, education should be about what you can do, and not what you can't.

We say, education is all about what you can't do.

That is what you go to school for.

To learn the things you don't yet know.

We are poles apart on what we believe.

, the shadow defence secretary, has suggested that, when the Tories talked about setting up an "Iron Dome", they were just using it as a generic term for missile defence – like describing a vacuum cleaner as a Hoover. They were not talking about the Israeli version, he claimed.

In an attempt to clear up the confusion caused by the Tories first saying they were proposing an Israeli-type Iron Dome, before Kemi Badenoch later said that wasn't the plan (see 7.59am), Cartlidge told the Press Association:

The phrase 'iron dome' has come to be used a bit like the word 'Hoover' to generically refer to missile defence systems – and this is clearly a missile defence system.

Is it the exact same iron dome as Israel? No.

The Israeli iron dome is a short-range system. It's to do with very near threats from the likes of Hezbollah.

It's just, if you speak to the media and the public, if you say 'iron dome', they at least know roughly what you're talking about.

, the shadow communities secretary, also spoke this morning to a near-empty hall. She said she was launching a programme to develop "a new Conservative vision for local government".

Explaining what that meant, she said:

That vision has to be informed by the wealth of experience that we have in our party.

Whether that's councillors, former councillors, or just people who know about their area, and who have ideas about how it should be run.

We want to hear from you.

And here is the latest edition of our Politics Weekly UK podcast. It features and talking about the Tory conference.

It is widely assumed that, under Kemi Badenoch's leadership, moderate, one-nation Conservatives have been more or less wiped out as a force in the party. But, in her Guardian column based on her time at the conference, suggests they might be more resilient than we think.

Here is an extract.

If nothing improves by next conference, the mirage of Badenoch's rock-solid support will melt away. But what would replace her? Waiting in the wings there is a model of what a Conservative revival might look like – Prosper UK, launched in January.

It tiptoes, praising Badenoch loudly, yet it is running seven events at this conference. That included a small Sunday night rally for electoral reform. It was addressed by former West Midlands mayor Andy Street, now co-chair of Prosper UK with Ruth Davidson It is backed by a formidable array of what was once the One Nation group, now defunct in parliament – or dormant under Badenoch's rightwards march. No MPs back Prosper UK in public, but the group claims a third of them do secretly, along with 30,000 declared supporters. David Gauke, vice chair, has crept back into the party – he thinks by accident when the membership computer processing his re-application didn't register he'd been ejected in 2019. In returning, he joined a battalion of remainer luminaries of the centre-right who'd had the whip suspended at the same time, including Kenneth Clarke and Dominic Grieve.

Gauke travels the country speaking to Conservative associations and others. Prosper UK is pro-EU, pro-migration for skilled workers and foreign students, pro-net zero and against the pension triple lock – and Gauke says that "Conservatives should be truth tellers on all these". But though socially liberal, he's dry as a bone on fiscal discipline, campaigning for low business taxes, a smaller state and enticing back non-doms – all Hayek, no Keynes. "No one speaks for some 7 million people centre or centre-right," he says.

And here is the full column.

In her interview with Times Radio this morning, hinted that, if Labour has legislated to make the pensions triple lock less generous by the time of the next election, a future Tory government would not reverse that.

In his party conference speech last week, Andy Burnham said he wanted to change the triple lock uprating mechanism from 2030, with the savings used to part fund his plans to set up a National Care Service. The government later said it would legislate for this before the election.

The Tories are committed to the pensions triple lock in its current form. But, asked if she would repeal any legislation passed making it less generous, Badenoch replied:

I have said that the triple lock is our policy and it remains our policy. I don't think going after pensioners is the right thing when there are loads of people who can work, who won't work.

When we are going to reverse Labour's policies, I say we are going to reverse their policies.

I have said that we are keeping this policy, but if they take that money and they spend it on something that we can't get it back from, then it would be difficult for me.

What I'm not going to do is lie to your listeners just so I can get votes. I tell the truth and I say the triple lock is our policy and we're keeping it.

But what I'm not going to do is to say something when I don't know what the situation would be about what Labour has done with that money. We have to be very careful.

, the education secretary, has given a speech at the conference. This morning the events are on the main stage, which is the smaller venue. This afternoon events are in the larger symphony hall.

Trott's speech was largely a long rant about supposed political correctness excesses in schools, with pupils being told that white people are privileged, women can have penises, Britain is racist etc. She said the Tories would "keep political activism out of the classroom".

Trott is now taking part in a panel discussion including the Telegraph journalist and GB News presenter . Tominey is no leftie, but even she seemed to think Trott had laid it on a bit too thick. Tominey said that, following the supreme court judgment, she thought children were no longer being told women can have penises.

There aren't many people watching – either in the hall or on YouTube, where there is a live feed.

But the Labour press office is tuning in. It has just posted this picture of the event on social media with the heading "People disguised as chairs latest" – a reference to a joke told by Jeremy Clarkson yesterday, when he was sarcastically commenting on how good it was to see so many people in the audience for his Tory conference session.

, former deputy commander of RAF Air Command, told Times Radio he did not think the Tories pledge of £10bn over 10 years would be enough to fund a missile defence system that would protect the UK, its territories and bases.

As the Press Association reports, Bagwell said:

It really is a question of definition of what capability you're going to deliver here, and what you can realistically expect in terms of protection.

You might be able to protect certain key sites, certain strategic areas. London would be an example, but of course that's not enough.

If you've got military bases all around the country, you've got power stations, you've got critical infrastructure dotted around the country, then you're really going to have to try and cover the entire area, which is is challenging.

Bagwell said a full system could cost more than £80bn. He said that the US was talking about spending between $200bn and $1tr (£150bn to £750bn) for their "Golden Dome".

Bagwell's analysis matches what General Sir Richard Barrons told MPs in the summer. (See 10.23am.)

According to the BBC, , a senior fellow at the defence thinktank RUSI, said that while £10bn would not fund an Israeli-style "Iron Dome" missile defence system, it would "probably cover" what the UK "actually needs" including horizon radar and more E7 aircrafts.