A powerful standards watchdog has accused Boris Johnson of failing to allay fears that he and his ministers consider themselves above the rules, as his support continued to ebb away in the wake of the Partygate scandal.

Jonathan Evans, the chair of the committee on standards in public life, criticised a planned overhaul to the way the ministerial code is policed, saying they undermined the role of Boris Johnson’s ethics adviser, Christopher Geidt.

His remarks came as two more Tory MPs wrote to their constituents condemning the prime minister’s conduct during the pandemic.

Downing Street announced the changes last week, after Evans’s committee made a string of proposals earlier this year.

The changes slated by the government include allowing ministers to escape resignation for minor infractions – but not giving Geidt the power to launch his own investigations without the prime minister’s permission, as the committee on standards had urged.

Evans, a former head of MI5, said it was “highly unsatisfactory” that Johnson had only accepted part of the package of reforms, and the plans as they stood would not “restore public trust”.

Unless Geidt can launch his own investigations independently, he said, “suspicion about the way in which the ministerial code is administered will linger.”

Johnson defended his conduct in a tough interview with the online forum Mumsnet, which kicked off with the question, “Why should we believe anything you say when it’s been proven you’re a habitual liar?”

During the exchange, Johnson said he was “very, very surprised and taken aback” to be fined by the Metropolitan police for his surprise birthday party, which he called a “miserable event”.

He said he was not considering resigning. “I just cannot see how actually it would be responsible right now, given everything that is going on, simply to abandon … the project on which I embarked, to level up.”

Geidt came close to resigning on Tuesday over Johnson’s failure to explain why he believed he had not broken the ministerial code when he received the fixed-penalty notice. A cabinet source insisted on Wednesday that Geidt was “definitely not resigning”.

Evans said he agreed with Geidt that Johnson’s reforms to the standards system displayed a “low level of ambition”, and would not fix the problem that a prime minister can simply disregard any recommendation from his ethics adviser.

“The new arrangements fail to address the risk of what Lord Geidt describes as a ‘circular process’: an adviser who believes their advice will be rejected will simply not put forward advice at all, with the precedent already established that this will lead to the adviser’s resignation.”

Even before the Partygate scandal, Johnson’s government had been accused of undermining standards in public life, including by overruling the finding of Geidt’s predecessor, Alex Allan, that the home secretary, Priti Patel, had bullied staff, albeit inadvertently. Allan resigned in protest.

Tim Durrant, associate director of the Institute for Government, said: “The ministerial code and Lord Geidt’s role has definitely been damaged by everything that’s happened over the last couple of years. The fact that behaviour and propriety have been such an issue for this government has really exposed the limits of the code, and of Lord Geidt’s role.”

The drip, drip of Conservative MPs publicly deploring Johnson’s conduct continued on Wednesday, with many at Westminster convinced that the threshold of 54 letters needed to trigger a vote of no confidence in him could be met as soon as next week.

Some MPs are known to be holding back from submitting letters of no confidence in Boris Johnson over fears that their names will leak and they will face reprisals from the whips.

Rebel Conservatives trying to orchestrate enough names to oust the prime minister say many MPs, particularly newer ones, are concerned about the privacy of the process. Simon Fell, the MP for Barrow, became the latest backbencher to publicly question the prime minister’s position, saying an apology was “insufficient” in a letter to constituents.

Fell, who was elected to Barrow, a “Red Wall” seat, in 2019 and was part of the “pork pie plot” of MPs who met to discuss their loss of faith in Johnson earlier in the year, stopped short of saying he had written a letter of no confidence in the prime minister.

“I’m left feeling angry and disappointed. It beggars belief that when the government was doing so much to help people during the pandemic, a rotten core with an unacceptable culture carried on regardless of the restrictions placed on the rest of us,” he wrote in a letter to constituents.

He was joined by Gosport MP Caroline Dinenage, who wrote to constituents that she was deeply concerned by the Gray report’s findings and suggested she had significant scepticism about changes in No 10.

“I am clear that systemic change is needed. The prime minister has stated that measures have been put in place to achieve this, but until I see real evidence of leadership that is listening and changing, I’m afraid I am not prepared to defend it,” she wrote.

Geidt used his annual report, published on Tuesday, to pose what he called the “legitimate question” of whether Johnson had broken the ministerial code in receiving a fixed-penalty notice for breaching lockdown rules. The code includes an “overarching duty” to comply with the law.

The prime minister, who is the ultimate arbiter of the ministerial code, then published a letter in which he exonerated himself on several grounds including the fact that he had apologised, and did not believe he was breaking the rules at the time.

He also stated that he believed the principles of good conduct in public life, which include selflessness and integrity, remained “the bedrock of standards in our country and in this administration”.

Johnson still faces an investigation by the House of Commons privileges committee over whether he lied to MPs when repeatedly asserting that “all guidance was followed” in Downing Street.

Despite the changes to the ministerial code, the penalty for misleading parliament remains resignation.

The committee on standards in public life is an independent body advising the prime minister, set up by John Major in the wake of the cash-for-questions scandal.