The move to launch an inquiry into Zahawi’s tax affairs – after it emerged he paid a penalty to HMRC over previously unpaid tax while he was chancellor – was designed to relieve some of the pressure. But No 10 knows that the prime minister, rather than the ethics adviser he has asked to establish the facts, will have to make the final call. For, regardless of the “due process” that Sunak has stressed he wants to follow, the decision about whether to dismiss Zahawi will be a political one.

Sunak’s own reputation is on the line. His vow to restore integrity and accountability to the government was mocked at prime minister’s questions and many Tory MPs question why he is burning through political capital when they feel fatalistic about the outcome.

“There will inevitably be terminal action,” a minister said confidently.

As well as the row over the party chair’s tax penalty, a long-running investigation into the deputy prime minister, Dominic Raab, over bullying claims continues. Though Raab denies the claims, the fact there are two major unresolved issues concerning ministerial standards has allowed Sunak’s opponents to call into question his judgment for letting them continue serving in the cabinet.

Sources close to Sunak are confident that letting the investigations take their course is the best approach. “Stepping towards a politics where actually the first lever that we pull isn’t the one that sacks someone is better in the long run,” said a government insider.

There is nervousness about a repeat of the bad blood that was created when the then trade minister Conor Burns was sacked in October over allegations of inappropriate behaviour, before being cleared two months later.

However, while those close to Sunak stress he wants a healthier political culture where people accused of wrongdoing are properly investigated, there is equal frustration that Zahawi did not do what they believe was the honourable thing.

“He’s the bloody chairman, he should appreciate the damage he’s doing to the party,” said one frontbencher. “A lot of us don’t understand why we’re taking this damage and he hasn’t made this easier for Rishi and just quit.”

Conservative MPs report their postbags and inboxes are not yet filling up with outraged messages, and say it has hardly been mentioned on the doorstep when they head out campaigning or speak to constituents.

They are also trying to heed the message handed down by the Tory strategist Isaac Levido at the Chequers summit, where cabinet ministers were gathered for a series of strategy meetings on Thursday. “Isaac is crystal clear we have to have party unity,” said one insider.

So far, the number of Tory MPs who have put their heads above the parapet remains relatively low – the most high-profile being Jake Berry, who has shown himself unafraid to be a thorn in the side of Sunak’s government.

Most of the grumbling is taking place privately, though MPs are uncomfortable they are heading into a second weekend expecting more embarrassing allegations to emerge about Zahawi and the issue of who knew what about his tax dispute.

Government whips, who rang around MPs after the story about the Zahawi tax penalty emerged, report a growing number of their flock are getting disgruntled at the handling of the issue.

Resisting a swift sacking would enable Sunak to avoid yet another aggrieved former minister causing trouble for him on the backbenches. Should a damning verdict come back about Zahawi’s actions, the prime minister can say his hands are tied.

To help calm jitters, messages of reassurance have been dispatched that the inquiry by Sunak’s ethics adviser into Zahawi will be over quickly.

There is already talk of who should be lined up to replace Zahawi and Raab, should they both be forced out. A number of close Sunak allies with cabinet experience remain on the backbenches, waiting for a chance to be parachuted into government and help avoid a more complicated reshuffle.

But with no definitive deadline of when the two investigations will be resolved, time remains of the essence. As one senior Tory sighed: “We’re getting closer and closer to the general election, we can’t afford to waste energy and time on this sort of stuff.”