Ever since Rishi Sunak became Prime Minister, his aides have worried that May would be the month of mutiny. His mandate over the party has always been weak, since he lost the summer’s leadership race to Liz Truss. He was also certain to preside over heavy losses in the local elections, so the aftermath of that defeat was seen as the ideal time for a rebel to strike. As if to tempt fate, Sunak invited more than 200 Tory MPs for drinks in the No. 10 garden on Monday night. He attempted to lift spirits with jokes at Keir Starmer’s expense.

‘He was meant to be writing a book about his ideas for Britain,’ Sunak said. ‘But – and I’m not making this up – he has had to return the advance to the publisher because he couldn’t come up with any.’ His guests laughed, but a few grumbled that Sunak himself gives a good impression of someone running out of ideas.

As disgruntled as some Tory MPs might be, there is nothing approaching mutiny in the backbenches. Even the whispers about a Boris Johnson restoration have fallen silent. Johnson was notably absent at the inaugural meeting of the Conservative Democratic Organisation, a pro-Boris group, on Friday night. One MP says the venue was a third full. ‘It was more of a postmortem of the past 12 years than a rally for his return,’ says one attendee. For now, at least, Sunak’s hold over the party is assured.

Yet the results of this month’s elections confirm what bookmakers say: that the Tories are on course for defeat. Attention is turning to what will come next for the surviving Tory MPs in the event of a Conservative loss next year. There are plenty of MPs who have an opinion about what the Tory party should look like in opposition – and who should lead it.

In a case of awkward timing for No. 10, this week ministers and MPs gathered at the National Conservatism conference in Westminster. The event – which has come over from the States – offered a platform for rival Tories to set out their vision. ‘It’s unhelpful,’ sighs a minister. ‘All the loudest colleagues suddenly have an audience.’

Michael Gove’s comment on stage that ‘There simply aren’t enough homes in this country’ led the former cabinet minister Jake Berry to shoot back at the Housing Secretary: ‘If only you knew someone with the power to do something about it.’ After Suella Braverman used her speech on curbing legal migration to blast the ‘totalitarian tendency of the left’, Gove charted a different course for the future by arguing that his party would not win an election with culture wars. ‘It’s rats in a sack,’ complains one minister of the spectacle.

Braverman attracted particular criticism on the grounds that her speech hinted at active leadership ambitions. Robert Buckland – the former Welsh secretary – launched a counter-attack: ‘I’m saying to the Home Secretary that she has got a big job to do. Getting on and doing that job is exactly where she needs to be.’ ‘Robert Buckland can bugger off,’ responds one Braverman ally.

While Braverman may be dipping her toes in the water of a future leadership bid, her more immediate aim is to shape the conversation on immigration numbers. Sunak wants to focus on controlling illegal migration (‘Stop the boats’) before considering wider decisions on border control. Braverman is fighting a lonely crusade for using Brexit powers to reduce overall numbers, and she has clashed with Chancellor Jeremy Hunt and Education Secretary Gillian Keegan on the issue.

While some in Downing Street find the Home Secretary a handful, she does have support. No. 10’s deputy chief of staff Will Tanner – a former Home Office aide – spoke in favour of tighter immigration policy before he entered Downing Street. He wrote an article in response to reports that Liz Truss would relax visa restrictions for low-skilled workers. ‘Far better to reduce low-skilled migration, drive up growth and wages, and honour your promises to voters,’ he argued. Braverman is holding the flame of what was, not so long ago, basic Tory policy.

In one of the stranger developments in Tory leadership intrigue, Penny Mordaunt is also being talked up as a contender after she held a procedural sword perfectly upright through the coronation ceremony. ‘It could be third-time lucky for Penny,’ says one MP. ‘She now has national prominence.’ Others are less impressed. ‘If we are about to pick the next leader based on them carrying a sword, we really do deserve to be in opposition,’ says one former minister.

The other bookies’ favourite is Kemi Badenoch. She has been under attack from the European Research Group after the government ditched the plan to repeal thousands of EU laws, saying it was only safe to discard 600. But she handled the rebels with her trademark bluntness – in effect, gathering them in a room and telling them to grow up – which may still work in her favour. ‘She can pitch herself as the pragmatic Brexiteer,’ says one MP. ‘There are more of those than there are Bill Cashes.’ Others suggest that Priti Patel, who has never yet run for the leadership, could be a surprise bet.

But all this is deeply theoretical, which is better than Sunak hoped for a few months ago. Given that the Labour lead has almost halved under his leadership, there’s still hope that he can steer the party to victory – but he has much yet to do. ‘What has consolidated the unhappiness is a fear that there aren’t enough dividing lines with Labour,’ says one senior Tory.

In a sign that No. 10 is aware of the issue, the Prime Minister invited the 1922 policy chiefs – the Tory MPs elected to represent the backbenches on key policy issues – to meet with cabinet on Tuesday. He was asking for contributions (an indication, perhaps, that he would also struggle to fill a book with his own ideas). He has survived the first phase of his leadership which is, given how things were last summer, no small achievement. But to survive the next general election, he will need all the help he can get.