Rishi Sunak’s appointment of Suella Braverman as home secretary showed he is not afraid to make controversial appointments to placate politically useful colleagues. Now the heat is on Gavin Williamson, the prime minister is fighting on two fronts. A forced resignation just weeks into his premiership might look embarrassing and reflect badly on his judgment – but the public may accuse him of that anyway if he attempts to stick by the Cabinet Office minister, who is accused of bullying behaviour. Despite Downing Street’s insistence Sunak has full confidence in Williamson, MPs believe the bid to stand by him is politically short-sighted given they think the revelations so far are just the tip of the iceberg. “I’ve got screenshots too,” said one backbencher, referring to the sweary texts Williamson sent to the then chief whip Wendy Morton earlier in the autumn. So why is Sunak expending political capital defending a minister who is far and away the least popular member of the cabinet, according to the closely watched popularity league table run by Conservative Home? Given the way Sunak has stood by Braverman, it is clear the new prime minister does not want to cave in to pressure. “Once you let one go, it sets a precedent,” said an MP. “That becomes the bar all future ministers would have to resign for clearing.” It also arguably benefits Sunak to have a few “lightning rod” figures that soak up most of the attention – diluting the intensity of the spotlight that might otherwise be being shone on next week’s anticipated tax rises and spending cuts worth up to £60bn. But if this is the strategy, it jars with what he has said in public. In his first speech on the steps of No 10, Sunak vowed his government would restore “integrity, professionalism and accountability at every level”. Some Tory MPs are not buying the excuse that Sunak is waiting to take a decision before the various investigations into Williamson are concluded. “They could take years,” one former whip said. Scepticism about the decision is high because of the way Conor Burns was sacked as a trade minister last month over reported allegations, which he denies, that he touched a young man’s thigh in a Tory conference hotel bar. He was forced to stand down while an investigation was carried out, while Williamson remains in post despite being the subject of at least two inquiries. Senior party figures also think Sunak believes the row over Williamson is a “Westminster bubble story”. Williamson was installed for a reason, and removing him would come with costs to the revamped Downing Street administration. Partly, it was envisaged that a wide-roaming brief in the Cabinet Office – the full details of which were not confirmed until Tuesday, two weeks since his appointment – would give Williamson the flexibility to quietly reprise his former role of chief whip. Working with the real holder of that role, Simon Hart, the pair could act as a “good cop, bad cop”. Having done a lot of backroom work for Sunak during the summer leadership contest, Williamson proved his worth by helping propel his candidate to be the frontrunner and get the most endorsements from MPs. Williamson is also heralded by many as a master of the “dark arts” and there are some Tories who believe Sunak brought him into government to avoid the man famed for having a pet tarantula working against him from the backbenches. But an uncomfortable theme is emerging about the people Sunak is standing by – given Williamson was sacked after being accused of leaking from the national security council – which he also denied – and Braverman’s leak of confidential Home Office information. A senior MP said the prime minister was “surrounding himself with people who have a known track record of national security issues”. If Williamson is forced out, there will at least be one silver lining for Sunak. One backbencher said: “It’s not like the role needs replacing so it won’t open up a potentially messy wider rejig.”