Five weeks after becoming prime minister, Rishi Sunak has discovered how hard it is to govern the country when you have an ungovernable party. The prime minister is battling backbench rebellions over housebuilding, onshore wind, tax rises, his China policy and the Brexit trade deal. His faction-ridden MPs have ignored his initial “unite or die” message, making his working majority of 69 an illusion.

The constant noise oft undermines Sunak’s unique selling point — competence. With the cost of living crisis prompting a wave of strikes, he does not look in control of events; mostly likely because he is not. Jacob Rees-Mogg, dropped from the cabinet by Sunak, has warned that the backbench revolts are “ill-advised”, adding that MPs must support their leader if they want to win the next election. But Rees-Mogg also said in public what many Tory MPs say in private: Sunak does not have a mandate because he was not elected by voters. “The mandate is important, and the mandate was Boris’,” he said.

Nor was Sunak elected by the Tory grassroots. Indeed, he has quickly tumbled down the popularity league table of Tory members in today’s ConservativeHome poll – from fifth place with a net positive 50 per cent satisfaction rating, to sixth from bottom on 9 per cent. Like Tory backbenchers, members are disgruntled and impatient about the small boats crisis.

Many Tories demand “grip” but their rebellions make the task of displaying it harder. Allies of Boris Johnson and Liz Truss are happy to join in; they have convinced themselves (wrongly) that Sunak plotted against them. The ranks of the former and never-to-be ministers have swelled after 12 years in power; they are semi-detached, and cannot be relied upon. Government whips also have little control over the growing number of Tories who have decided to stand down at the next election; they have nothing to lose now.

How do you govern when you have such a fractious party? All of Sunak’s options come with problems. He could remove the whip from some troublemakers, as Johnson purged 21 pro-Europeans. But removing the whip from eight Eurosceptics in the 1990s didn’t work for John Major; they became martyrs in the party and were allowed back into the fold six months later.

Today’s rebels are not a homogeneous bloc; there is a sizeable minority of different MPs ready to revolt on different issues. If Sunak tried to disprove Keir Starmer’s “weak” jibe by “taking on” hardline Eurosceptics and softening Johnson’s hard Brexit, he would provoke a civil war; ardent Brexiteers would warn he would suffer the same fate as Theresa May. Sunak could go soft and make concessions to the majority of his MPs on any given issue. But that would reinforce Starmer’s attack on a leader at the mercy of his backbenchers who puts “party before country”. In any case, there’s no guarantee Sunak could buy peace. Tory MPs are good at pocketing concessions and then demanding more as they move on to their next hobbyhorse; that would feed the media narrative about revolts and U-turns. Plans to allow more housebuilding — critical to the Tories’ ability to appeal to younger voters — have already been diluted once. The current rebellion is against the proposed compromise.

Another option for Sunak would be to collaborate with Labour to outgun the Tory rebels on some issues. If the PM changed tack to allow more onshore wind, Labour would support him. Sunak could argue he was acting in the national rather than party interest, and voters might like such cooperation. But opposition parties are unreliable partners, and there would be a backlash among Tory MPs for sleeping with the enemy. Johnson’s hopes of staging a counter-coup against Sunak next summer would rise.

So Sunak will try to muddle through.