Conservative party chair Oliver Dowden has insisted there is a “strong case” for Boris Johnson to remain as prime minister, despite growing backbench anger over the government’s handling of the partygate scandal and fears over upcoming local elections.

Johnson now faces three probes into the allegations of rule-breaking throughout the pandemic: the House of Commons privileges committee, which will be led by senior Tory Sir Bernard Jenkin; Operation Hillman, the Metropolitan Police investigation; and the inquiry by civil servant Sue Gray.

Dowden said on Sunday that he recognised the “legitimate hurt and anger” of the public over the issue of partygate but argued that the “uncertainty” caused by a change of leader at this time “would be dearly damaging” to the country.

“I think the prime minister is doing a really important job — whether that is what you saw in India this week in terms of agreeing the trade deal, continuing to tighten the pressure in Ukraine — so I think there is a very strong case for the prime minister remaining in office,” he told Sky News.

This sentiment was echoed by Jacob Rees-Mogg, minister for Brexit opportunities, who in an interview with GB News argued that Johnson had got “many of the decisions right” in recent months, adding that the prime minister still had his support and that of the public.

“I don’t think people are losing faith in him, the socialists don’t like him, of course they don’t, that’s their job,” he said.

However, the latest polling by YouGov has revealed growing public scepticism over Johnson’s handling of partygate. Some 78 per cent of those surveyed believed that Johnson lied in his explanations to the public over rule-breaking in Downing Street and Whitehall.

Questioned on whether Johnson ought to quit if found by the privileges committee to have lied to MPs in the chamber, Dowden said he did not believe that Johnson had misled parliament, adding: “He is perfectly open to the privileges committee to conduct that investigation and parliament consented to that, so I don’t believe that scenario will arise.”

Ahead of local elections on May 5, which come at a time of tax increases and rising prices, Dowden admitted that the Conservatives may struggle. “Of course, we’re midterm anyway. They will be a challenging set of elections”.

In recent days, Conservative MPs have publicly and privately voiced concerns over the prime minister’s leadership following the decision by the Met to fine him £50 for his attendance at a gathering in June 2020.

Steve Baker, a former minister, told parliament last week that Johnson “should be long gone”. Senior backbencher William Wragg confirmed that he had submitted a letter of no confidence last December and said that Tory MPs were finding it “ utterly depressing” to “defend the indefensible”. 

Labour leader Sir Keir Starmer said on Sunday that he was not going to “shy away” from the fact that Johnson has become the first prime minister to be found to have broken the law in office, as he defended Labour’s focus on the partygate scandal.

“His moral authority, his authority to lead, is shot through and his own side have now had enough of defending him,” he told the BBC.

However, he said that he also recognised that the cost of living was the most pressing concern for households across the country, adding that Labour had proposed measures aimed at supporting families.

“That is the single number one issue for so many people and they’re really struggling to pay their bills, and the response of the government in the Spring Statement was woeful,” he said.

Labour have called for the government to introduce an emergency Budget to address the crisis.

Meanwhile on Sunday, the Tory party was embroiled in another internal row after the Mail on Sunday published a story which cited an anonymous MP accusing Angela Rayner, Labour’s deputy leader, of using “Basic Instinct” ploys to distract Johnson in the Commons, referring to the 1992 film starring Sharon Stone.

Following a backlash from Rayner and other Labour figures, Johnson and some members of his cabinet condemned the story. “I respect her as a parliamentarian and deplore the misogyny directed at her anonymously today,” the prime minister wrote on Twitter.