Rishi Sunak walked into the House of Commons to a cheer that was intended to sound resounding, affirming and utterly convincing. It is the prime minister’s tragedy that in the context of his collapsed authority it sounded instead bitingly sarcastic. His MPs tried it again when he stood up and Labour MPs were so delighted that they shouted for more.

The Tory benches were busy, rather than packed. This wasn’t a mass stay-away of the sort that Boris Johnson experienced at his nadir, but there was a sense that quite a few Tory MPs had decided the half-hour could more usefully be spent signing Christmas cards than listening to their leader.

Labour, on the other hand, were very jolly. Who can blame them? It’s two years since the Tories had a polling lead, Sunak’s popularity continues to plunge, and his MPs are at his throat.

The chamber was silent. This sort of thing is unanswerable

For the prime minister, these sessions are increasingly a wrestling match not with Keir Starmer but with the beast that lies within him. There are two Sunaks. One is genial, the polite Winchester head boy, smooth hedge fund salesman and kindly furlough funder who can charm a room. But not far beneath the surface lies Snippy Rishi, the stroppy teenager who is sick of being asked to tidy his room and is furious that his Xbox has been confiscated. Starmer’s goal at every encounter is to set Snippy Rishi free.

He began with a little gentle goading. “Christmas is a time of peace on earth and good will to all,” he began. “Has anyone told the Tory party?”

Sunak had a sort-of joke ready. “Well, Christmas is also a time for families,” he replied, “and under the Conservatives we do have a record number of them.” This was intended as a reference to the “Five Families”, the collective description of the party’s troublesome backbench factions, but its meaning wasn’t obvious. The prime minister could equally have been celebrating Britain’s high levels of immigration, or Boris Johnson’s personal contribution to the birth rate.

“Yet again,” Starmer said, “the Tory party is in meltdown and everyone else is paying the price.” Behind Sunak, government ministers gestured in outrage and disbelief, as though this was the most ridiculous thing they had ever heard. The Labour leader taunted them, quoting the things Conservative MPs had been telling the newspapers. “Who was it who said he is ‘a really bad politician’?” he asked, clearly enjoying himself. “Hands up? Well, what about ‘inexperienced’ — who was that? Or — there have to be some hands for this — ‘he’s got to go’?” Two rows behind Sunak, Theresa May allowed herself a quiet smile.

Sunak tried to laugh it off. “He should hear what they have to say about him,” he said. As comebacks go, it was more “your mum!” than Oscar Wilde. The session had an end-of-term air by now. On the back row, Tory MPs Gary Sambrook, William Wragg and Alec Shelbrooke were whispering to each other with a schoolboy air.

Starmer switched gear, pointing out that a record 140,000 children are going to be homeless this Christmas. “Rather than indulging his backbenchers swanning around in their factions,” he asked, “when will he get a grip and focus on the country?”

Sunak’s reply exposed all his weaknesses as a politician. “Let us just look at the facts,” he began. Up in the gallery, we sensed that Snippy Rishi was getting ready to emerge. “Rough sleeping in this country is down by 35 per cent since its peak, thanks to the efforts of this government.” Pressure of time prevented him from saying it was also up 74 per cent since 2010, also very much thanks to the efforts of this government.

Starmer went in for the kill, reading a letter to Santa written by an 11-year-old, asking for a “forever home”. The chamber was silent. This sort of thing is unanswerable.

Snippy Rishi is the person that Labour would very much like the public to meet, and the worse things get for Sunak, the snippier he becomes

And yet Sunak had to try to answer it. You can complain that it’s not fair to expect the prime minister to fix every tragedy across the country, and that is true. A year from now Starmer may in his turn be facing tricky questions about tragic stories. The best approach is to offer sympathy and empathy and point to what your government is doing. This was not the approach Sunak took.

Instead, he unleashed his alter ego. “If he really cared …” he began. Labour roared at the suggestion that Starmer was confecting his feelings for homeless children, but Snippy Rishi was ready to take them all on. “No, no, no,” he snarled. “No, no, no.” He had a point to make and he was going to make it.

Once he’s out, Snippy Rishi can’t be silenced. Indeed, there were signs of a previously unknown, even more furious person within. Raging Rishi? You won’t like him when he’s angry. Although these days the Tories don’t have much time for him even when he’s calm.

“If he really cared about building homes,” he went on, his voice becoming shrill as he complained that Starmer hadn’t voted for planning reform when he’d had the chance. It was not a bad point, but the point was lost in the terrible tone.

Sunak calmed down as the session went on, but it was too late. Snippy Rishi is the person that Labour would very much like the public to meet, and the worse things get for Sunak, the snippier he becomes.

Before the prime minister’s half hour was up his MPs had already begun to drift out, leaving big gaps on the benches behind him. It wasn’t a walk-out, just the continuing bleeding away of his authority.