We're going to leave our live coverage there - thanks for joining us.

Yesterday's Coronation marked one transfer of power - and our host Laura Kuenssberg has suggested that electoral results around England indicate another, political one could be under way as well.

We heard the culture secretary admit that the Conservatives had a "difficult" result. You can read more of her comments in our main story here.

The Lib Dem leader and Labour's shadow health secretary were questioned about their party's own results - and whether they'd consider working with one another in the event of a hung parliament after the next Westminster election. Expect to hear much more about that over the months to come.

Until next time, it's goodbye from us. This page was put together by James FitzGerald, Marita Moloney, Aoife Walsh, Sam Francis and Sam Hancock.

After an hour of spirited conversation on topics such as the local election results, the Coronation and even the BBC licence fee, this morning's programme left us with plenty to digest.

Here's a look at what we heard:

• Speaking about the losses the Conservatives suffered in Thursday's local elections in England, Culture Secretary Lucy Frazer admitted it was a "difficult result" for her party
• Lib Dem leader Sir Ed Davey and Labour's shadow health secretary Wes Streeting talked up their chances in the next Westminster election. Davey ruled out any possible coalition with the Conservatives, but when asked if would consider a deal with Labour, he was evasive and said it was a "hypothetical question"
• Meanwhile, Streeting insisted Labour could win a majority and said that was what the party was working for. He also said he didn't think proportional representation (an alternative voting system favoured by the Lib Dems) would be in Labour's manifesto
• Speaking about the police response to protests in London during the Coronation, Frazer said police had to make "tough calls" yesterday and would have made operational decisions on a case-by-case basis
• And - fresh from attending the Coronation himself - New Zealand Prime Minister Chris Hipkins was asked about his views on whether the monarchy should exist. He described himself as a "technical republican" and said it "would be nice" to have someone in New Zealand as the head of state

Sir Ed Davey has been talking up his party's own electoral chances - though he says he won't take people "for granted".

And here are more of those comments from the shadow health secretary on potential coalitions that could emerge from the next general election.

Wes Streeting says the Labour is not considering teaming up with the Lib Dems.

Laura Kuenssberg
Presenter, Sunday with Laura Kuenssberg

In contrast to Lucy Frazer, Labour’s Wes Streeting and the Lib Dems' Sir Ed Davey seemed to be competing to see who could be the more bullish.

They are both of course all too aware that the Conservatives would like to stir up a debate about their performance - and the prospect of a coalition after the next election.

But given how votes stacked up this week it is a legitimate political question to ponder whether they would work together.

Streeting said that changing the voting system would not be in the Labour manifesto. Traditionally this has been seen as the price to pay to get the backing of the Lib Dems in case of a hung Parliament.

Sir Ed Davey confirmed - no surprise - that the change would be in his own manifesto. The Lib Dem leader doesn’t want to talk about the hypothetical situation of another coalition - this time with Labour.

You‘ll have noticed he is happy to explicitly rule out working with the Tories again. When it comes to Labour, he does not.

What Labour hopes is that they will build so much support in the next year that a conversation about coalition will be irrelevant.

Much will be revealed in the coming months, and it’s of course down you.

Laura Kuenssberg
Presenter, Sunday with Laura Kuenssberg

"We are listening", said the culture secretary this morning in the wake of a dreadful set of election results for the Conservatives on Thursday night.

But there is no sign of any change in direction. Or any re-thinking of the government’s plans or pledges. Instead, a recognition that inflation is still making it hard for millions of people to make ends meet.

Frazer suggested that there had actually been some progress during the local election campaign in her part of the country.

Looking at the big picture however, I wonder if some people listening to the cabinet minister this morning might conclude the Tories are in denial about how serious the situation for them is.

In the UK for the King's coronation, New Zealand's leader Chris Hipkins was asked by Laura Kuenssberg whether he believed the monarchy should exist.

He went on to describe himself as a "technical republican", saying he'd prefer his country's head of state to be someone who was actually in New Zealand.

But Hipkins admits there's not currently "a groundswell of support" for change.

Image source, Reuters

We heard our guests talk about yesterday's anti-monarchy protests - and how these were handled.

Human rights groups have criticised the police response as being "deeply concerning" - after the Metropolitan Police arrested 52 people in London.

Among them were Graham Smith, head of protest group Republic - which wants to scrap the monarchy and elect a head of state. Smith claimed he was arrested despite working with Scotland Yard to ensure the demonstration was legal.

Human Rights Watch said the police's actions were "something you would expect to see in Moscow, not London". Amnesty International raised its own concerns as well.

MPs gave their views, too. Shadow minister Jess Philips tweeted: "Our nation and our King is not so fragile as to not be able to take harmless protest of a different view".

The Met said it "understands" public concern, but that officers had acted proportionally under the law.

No arrests were reported outside London. Other protests happened in Cardiff, Glasgow and Edinburgh.

Read more here.

Here's the moment the culture secretary insisted "we are listening" after a drubbing at the polls during Thursday's local elections in England.

If you were having a lie-in or missed the programme for any other reason, you can watch back below.

We'll also be recapping some of the top lines on this page.

There's just time for a final word from the panel before the show wraps up.

Sir Ed Davey gets the final word, saying it's the "responsibility" of his Liberal Democrats and other parties to put forward a "positive case" ahead of the next general election.

Asked about whether Labour would back an apology for the effects of British colonisation, Wes Streeting "we should be honest and open about the terrible injustices".

"We have to view British history in the round," he said, including the "highs and lows and everything in between".

He points out that former Labour prime minister Tony Blair apologised in 2007 for Britain's role in the slave trade.

Streeting's now being asked about the anti-monarchy protests yesterday, on the day of King Charles' coronation.

Asked if he's uncomfortable with how the protests were handled in London, he says he feels "reassured" that the Met Police can recognise that there's a "gap" between the public and confidence in the police.

He says it's important to acknowledge that people "can disagree" with the monarchy and the Royal Family, and that the protests are an example of the country's "democracy".

"We'll wait and see if they got balance right," he says - adding that the Casey Review shows that it's "important to hold hands up" where appropriate.

More now from Labour’s Wes Streeting, who's asked if Labour would consider any potential coalition with the Lib Dems in Westminster.

He says Labour thinks it can win a majority and that's what the party is working for.

Pushed on whether he would rule out a coalition with Lib Dems, he says Labour is "just not in that ballpark of talking about coalition governments."

Asked if he would offer the Lib Dems proportional representation (an alternative voting system), he says he doesn't think that would be in Labour's manifesto.

Across the studio, Sir Ed Davey affirms that it will be a Lib Dem policy proposal.

Wes Streeting reiterates that he's "confident" Labour will form the next Westminster government after this week's local elections.

He admits local elections are "not a prediction of the next general election". But he believes many people who voted for smaller parties this week will switch to Labour at a general election.

He is probed on figures that suggest Labour's vote share didn't shift for Thursday's local elections in England.

The "best is yet to come," from Labour, he claims.

Streeting talks about Labour's "gains" in the recent local elections, saying "whether it's in the south of England, whether it's in the north of England... Labour is winning back support".

The shadow health secretary adds that his party is "confident" but not "complacent".

Laura probes the Labour MP on party leader Sir Keir Starmer's suggestion that the results mean his party is on course to win a majority at the next general election. She says the figures show this isn't quite the case.

"Laura, I honestly think we could be sat here on election night... Keir Starmer could be on his way to Downing Street [as the new prime minister] and the Conservative talking points would still be 'disappointing night for the Conservatives but Labour could've done better' - come on," he says.

We're now hearing from Labour's Wes Streeting - we'll keep you posted with what he says.

Davey is asked about his relationship with the Conservatives and if he would work with Sunak under any future coalition.

He says no, and says that he spent "all my life fighting the Conservatives" and that when he became leader he pledged to get the Tories out of government.

Probed on whether he would consider a potential coalition deal with Labour, he says it's a hypothetical question.

He adds that the Lib Dems are "not going to take the voters for granted" and that they have to earn their support.

Liberal Democrat leader Sir Ed Davey claims his party's list of target seats for the next general election will "almost certainly getting longer" after winning hundreds of new council seats.

He said Liberal Democrats successes at the local election were down to both "local issues and national issues".

“People were saying time and time again it was the Conservative policy on NHS and the cost of living," he says.

"The other big issue was integrity. There was a feeling the Conservative Party had lost its way.”

We're hearing from the panel now on whether a reparations process or an apology from the government or the Royal Family should be considered.

Asked if an apology would make a difference to the community relations within the UK, Prof Jason Arday says thinking about "the language that is used with those communities" and the apology that is "so sought-after" would go a long way to modernise the Royal Family.

Next up is Daily Mirror editor Alison Phillips, who is asked if she thinks a Labour government would do it. She says yes, and she thinks the King is moving towards a point where that happens.

Davey agrees with the panel and says the King is moving towards looking at this issue with "greater subtlety" that we're seeing from the government.