he hottest ticket at Labour conference – after Andy Burnham's speech – was an afterparty in Liverpool's Baltic Triangle, headlined with a set by the noughties girlband Sugababes. As Labour activists and ministers belted out the lyrics under pink spotlights, it was hard not to draw some parallels with the party's recent history.

There have been painful lineup changes and a lot of internal division, but this week onstage in Liverpool the originals are back together and they only played the hits. The fans can't get enough.

Burnham's own show on the main stage had the conference hall in raptures not because of Brexit or social care but because of the display of raw emotion after the tightly choreographed repression of the last six years. He may as well have walked across the stage with his feet crunching over the debris of shattered Ming vases.

The speech combined plans that had been forming inside Burnham's head for the last decade as well as seat-of-his-pants political instinct. On the morning of the conference, the prime minister took off early for a morning jog and then returned to make final amendments. Even moments before he went on stage, he was still rewriting, aides said. About a quarter of the speech was entirely ad-libbed.

When Burnham was rehearsing the speech, aides said, he knew he was going to cry when he got to the paragraph about his late father – he never managed to get through any of the practice runs without tears.

But the long pause as he composed himself was the most emotional he had been. Several ministers said they themselves had been moved to tears, including Ed Miliband, who had recently lost his mother, as well as Louise Haigh and Anneliese Midgley, who are Burnham's closest friends in government and the architects of his ascendancy.

After his speech, Burnham gathered all his ministers for a private pep talk. He said he knew they would not agree with everything, but – with the aura of a general sending his troops into battle – he told them to "get out there" and fight for it. He said he would not send them out with "a pea-shooter" – they needed proper weapons for the fight ahead and he promised he would provide them.

In the hallway outside the conference hall, minister after minister spoke with voices quivering with emotion. "This is all I have ever wanted," one said.

The bar for speeches from political leaders has been low for the past decade or more. It is rare for clips to be anything more than a soundbite for social media and then a long shopping list of statistics and achievements. Burnham's was the first time many MPs can recall a speech that was pure political argument.

And there was much in the speech that in normal times would have been a recipe for rebellion: Brexit, the triple lock, electoral reform and the lingering question marks over growth and defence.

"I found parts of the speech challenging, if I'm honest," one cabinet minister admitted. "It contained things I had always thought we should never touch or an argument about public control which I would previously have said was too backward-looking. But in the room I agreed with every word because he persuaded us, he made an argument and made me question myself. It was a quite extraordinary thing."

Even within the cabinet, there are those who grimace at the idea of electoral reform. "But you know, he believes in it, and I'm going to swallow it," said one.

Burnham called his cabinet ministers in for a last-minute meeting just before the speech, where he laid out his private arguments and took their comments and feedback. "I feel almost embarrassed admitting this, but that has never happened before with any other leader," one said.

On the sidelines of the conference, when cabinet ministers are at their most candid, they sometimes talk as if they have been through a kind of collective trauma – and the Burnham ascendancy has given them the release they need to confess how hard they have found the last two years. There are close new friendships and alliances forged in the coup, which defy previous factional lines.

"There's the management-speak slogan: 'Culture eats strategy for breakfast.' Well, this is proof positive," one cabinet minister said. "The past two years were utterly miserable, almost every single thing we achieved was poisoned by petty fighting. Every meeting was a choreographed exercise in pointlessness. Now we are discussing ideas and politics among colleagues who respect and like each other. I look back and I am so overwhelmed with relief that we did this."

Another cabinet minister said: "I wasted so much of my own bandwidth fighting over the most puerile things, or defending my own staff who were being made miserable. Keir [Starmer] never dared to take it on."

Even veterans of the Starmer years said they found themselves persuaded despite themselves. "Feels like there's something quite psychologically profound about daring to take on the triple lock and finding that the planes don't fall from the skies," Starmer's former strategy director Paul Ovenden posted.

Darren Jones, the ousted chief secretary who has made himself the face of the awkward squad, was also quick to lavish praise. "[The speech] told the story of his politics and the type of Britain he wants to build," he said. "He told us we'd be in no doubt what his priorities are for the country, and he was right."

Burnham will not welcome the comparison, but the closest recent one is how it felt at the Conservative party conference in the pre-disgrace Boris Johnson years: an electric electoral prospect who can genuinely reach across the political spectrum, hypnotising his doubters by the sheer force of his personality.

But this prime minister has no hint of the sleaze or incompetence that was always in the shadows for Johnson. If it comes, Burnham's downfall will probably be his own voracious appetite for political risk – but that could also be the making of his premiership.