Adam Goldsmith
Live reporter

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Viewers saw two political heavyweights holding their own on Sunday with Laura Kuenssberg today - as the show interrogated AI, the UK's economy and the Southport killings.

Ahead of a big speech next week on spurring economic growth, Chancellor Rachel Reeves said that the government needs to "get a grip" on financial problems in the UK, and said Labour is "cracking on" with reform on AI and planning.

But amid opposition from environmentally-minded MPs and local residents who don't want an expansion, Reeves stopped short of confirming that a third runway is coming to Heathrow.

Kemi Badenoch then sat down in the Kuenssberg hot-seat, three months from her election as Conservative leader.

On the Southport killings, Badenoch said more needs to be done on social integration, citing her own personal experience as equalities minister.

Both the chancellor and Conservative leader also focused on the role of tech companies play in tackling extremism. Reeves said social media platforms have a “moral responsibility” to remove violent content, while Badenoch warned that young people should stay off smartphones.

Finally, Badenoch clapped back at a poll showing support for Nigel Farage’s Reform party ahead of the Conservatives’, saying that this simply reflected voters’ anger at the failures of the last government.

Thanks so much for joining us.

The expansion of Heathrow has long been opposed by green groups, some Labour MPs and residents living near the airport.

Sir Keir Starmer and seven ministers who attend his cabinet - including Energy Secretary Ed Miliband and Environment Secretary Steve Reed - voted against proposals for a third runway in 2018, when the party was in opposition.

Last week Miliband said he would not resign if the government backed a third runway, insisting clean energy was "absolutely complementary" with the government's growth mission.

But London Mayor Sadiq Khan has said his opposition to a third runway has not changed and he would support a legal challenge if the government backed proposals.

• You can read more about this story

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Sir Paul McCartney shared his thoughts earlier about AI's impact on creative industries, reflecting similar concerns raised by other artists like Sir Elton John.

Kuenssberg asked chancellor Rachel Reeves if her government would be willing to sit down with artists to discuss Labour's proposal to change copyright laws. The changes would allow AI developers to freely use music and art online to help develop their computer models, unless artists opt out.

"We've got to get the balance right," Reeves says, so that artists are "properly rewarded" for their content - but says that's not "incompatible" with attracting AI companies to invest in the UK.

Panel member entrepreneur Theo Paphitis also weighed into the AI discussion, saying legislative changes are desperately needed in the technology industry.

"Big tech companies taking huge, fabulous wealth out of our economy and not having social responsibility for their actions and not paying for it - we need to legislate now," he said.

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Badenoch has pointed to social integration as a factor in Axel Rudakubana’s stabbing attack at a Taylor Swift dance class.

But the topic of integration was absent from Mr Justice Goose’s decision to hand Rudakubana a 52-year prison sentence.

Instead, the judge focused on the evidence needed to prove an act of terrorism and arrived at the conclusion that although extremely violent, the stabbings did not satisfy the legal test required for a terrorist act.

“In his home the police discovered clear evidence of a settled intention to carry out mass killing,” he said. “On one of his computers were files proving that he had a longstanding preoccupation with violent killing and genocide.”

The judge accepted the prosecution’s argument that the killings were not an act of terrorism under the law, since there was no evidence that Rudakubana’s purpose was to advance political, religious, racial or ideological cause.

But, he said that the extreme level of violence was “equivalent in its seriousness to terrorist murders whatever his purpose”.

On today's show, we heard from Conservative leader Kemi Badenoch on the Southport attack.

"If you're being inculcated in hate, you're not integrating well", she says. You can listen to her full comments below.

Both guests spoke on how to respond to the Southport attack on this week's show. For Labour, a crackdown by Big Tech firms on violent content is one place to start.

You can watch what the chancellor had to say on the topic below.

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Kuenssberg earlier questioned Chancellor Rachel Reeves about Heathrow's third runway.

It's unclear if the government will approve the project - but the BBC understands Reeves could make an announcement about airports in a speech this week.

The idea of a third runway at Heathrow has been debated for nearly 20 years. It's been strongly supported by the aviation industry and business leaders but opposed by environmental groups.

Alongside Heathrow, the Treasury is also considering whether to approve a second runway at Gatwick and expand capacity at Luton Airport.

If any airport expansions go ahead, they would be "vital" for UK business growth, according to Shevaun Haviland, director general of the British Chambers of Commerce.

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During the programme, Rachel Reeves was pressed on the status of taxes for "non-dom" residents in the UK.

Non-dom describes a UK resident whose permanent home - or domicile - is outside of the UK for tax purposes.

It refers to a person's tax status and has nothing to do with their nationality, citizenship, or resident status, although it can be affected by these factors.

A non-dom only pays UK tax on the money they earn in the UK. They do not have to pay tax to the UK government on money made elsewhere in the world, unless they pay that money into a UK bank account.

For wealthy individuals, this presents the opportunity for significant and entirely legal savings if they nominate a lower-tax country as their domicile.

One of the most well-known non-doms is former Prime Minister Rishi Sunak's wife, Akshata Murty.

Labour had announced plans to abolish non-dom status in order to remove this loophole, and on today’s programme she stressed that people who make Britain their home should pay taxes here.

But, amid a campaign to encourage growth, the chancellor stressed that a white paper later this year will consider how to attract high-skilled people to contribute to the economy.

• Read more about what non-dom means and how the rules are changing

That's a wrap on this week's episode.

Reeves spoke about the economy and her first seven months as chancellor, while Badenoch also gave her review of the past three months since she became Tory leader.

Badenoch spoke extensively on the Southport attack and how government could prevent such attacks in the future. She says that social integration played a role in the stabbings.

Stay with us as we bring you more analysis and reaction about this week's show.

If you’re keen for more politics and analysis from Laura Kuenssberg, you can sign up to her Off Air with Laura K newsletter.

You’ll get expert insight and insider stories every week, emailed directly to you.

Kuenssberg asks Badenoch how many members the Conservatives have now.

Badenoch responds: "We do not really share the membership numbers."

She says she prefers to focus on things that matter, rather than party membership.

"Right now, I need to make sure that people can see that there is a new leadership that we're holding the government to account on all those issues that I mentioned," she says.

We're shown a graphic that indicates the Conservative party is behind Reform in the polls.

Badenoch says that the reason for this is because the Tories have just been kicked out of government last July.

She says people are angry and are protesting against the last government.

The Conservative leader says it is now her job to show the public that the party has new leadership, and to hold the government to account.

Badenoch is now asked why her party wants to ban smartphones in schools.

She says she "strongly believes" young people should stay off smartphones "ideally up until 16".

The Tory leader adds it's "very difficult to control" the information that a child gets and says she is "very tech savvy".

Smartphones weren't around when I was younger, she says, and adults are addicted to them - "so what chance do children have?"

Kuenssberg is pressing Badenoch on what evidence she has to suggest integration played a role in the crime.

Badenoch points to the sentencing, which revealed that Rudakubana accessed violent content online, as an indication there was an issue.

“I’m not scared to tell this hard truth. I believe that we need to be honest,” she says.

Kuenssberg asks if Badenoch would have overruled the CPS decision not to disclose certain information from the Southport case if she were in charge.

Badenoch says the public needs reassurance that the government is handling matters competently. She says an inquiry should examine the government’s response and what can be improved.

She adds she doesn’t know the specifics of the CPS advice, but would aim to reassure the public without jeopardising the trial.

The Conservative leader is pressed by Kuenssberg, who asks her to provide evidence that a lack of integration into society was the reason behind Rudakabana'a crimes.

Badenoch says that every time a politician tries to talk about issues of integration, there's a pushback about the language they use.

She says this sets the discussion back, and adds that she has seen lots of evidence from her work as minister for equality that more needs to be done.

"It's very difficult to get this kind of evidence, we do need personal experience, we do need anecdotes," she explains.

The discussion now turns to the Southport stabbings and Axel Rudakubana's 52-year sentence for the murder of three young girls at a dance class.

Kuenssberg asks Badenoch about her comments that it was absurd the UK was not talking about integration more. What did you mean by that?

Badenoch says the Southport killings "affected me really deeply" referring to her two daughters who love Taylor Swift.

"When it happened, I could just imagine it being them," she says.

She says there are people "like Rudakubana who are...not integrating into the rest of society".

Kuenssberg says integration usually means people from different religious or racial backgrounds and that Rudakubana was born in the UK. What's the evidence that his crimes were to do with integration?

My evidence is "my personal experience" as an African Christian, Badenoch says.

Kuenssberg asks the Tory leader what the main takeaway is for the public.

Badenoch says the Conservative Party is under new leadership and is taking a different approach.

She adds that politicians have been telling people what they want to hear.

“Labour did the same thing but came to power without a plan,” Badenoch says. “It’s about doing the right thing and being able to deliver, and that requires a lot of hard truths which we have not been discussing as a country for years.”

Kuenssberg points out that this is a very damning statement, even for her own party. Badenoch responds by saying she is loyal and has taken collective responsibility.

In the break between this morning's two political heavyweights, we heard from Sir Paul McCartney about the risks facing musicians amid an AI boom - there's more on that in Kuenssberg's chat with the Beatles star.

Now though, Conservative leader Kemi Badenoch is in the hot seat - three months after her successful leadership bid.

Asked if she thinks it's been a successful first few months, Badenoch replies that it's been "good", but says "success" will take some time.

Badenoch accepts that the Conservative party has made some mistakes, but says they are now an effective opposition and have pushed the government on their school bill. She also says they hope to push more on tackling gangs.

We're hearing now from Sir Paul McCartney, who says the government should do more to protect the copyright of musicians and artists so they aren't ripped off by artificial intelligence (AI) developers.

"I think AI is great, and it can do lots of great things," McCartney tells Kuenssberg.

The changes would allow AI developers to freely use music and art online to help develop their computer models, unless content creators opt out.

McCartney says "when we were kids in Liverpool, we found a job that we loved, but it also paid the bills" and the copyright changes could remove the incentive for artists and result in a "loss of creativity".

He says the government should protect artists: "So you know, if you're putting through a bill, make sure you protect the creative thinkers, the creative artists, or you're not going to have them."

• Read more from Laura's interview with Sir Paul in our full story