Boris Johnson should relinquish his right to decide when possible breaches of the ministerial code warrant investigation, according to the chair of the Committee for Standards in Public Life.
In a letter to the prime minister, Lord Evans argued the power to launch a probe into the behaviour of members of the government should instead be held by the next independent adviser on ministerial interests.
It comes as questions continue to mount over contacts serving ministers had with former prime minister David Cameron in relation to his lobbying on behalf of the now-bankrupt finance firm, Greensill Capital.
The post of independent adviser has been vacant since last November after the resignation of Sir Alex Allan.
He quit the role after Mr Johnson rejected his conclusions in an inquiry into bullying allegations against Home Secretary, Priti Patel.
In addition to giving Sir Alex's successor powers to initiate investigations, Lord Evans recommends they be supported by a "small secretariat, independent of the Cabinet Office" and be allowed to publish summaries of their findings independently.
He also argues that while the sanction for any breach should remain a decision for the prime minister, the "current expectation" that a breach should result in resignation was "disproportionate" and should be used only "where a serious breach has occurred".
Downing Street has not yet issued a response to the letter.
The intervention from Lord Evans comes after Labour claimed Health Secretary Matt Hancock may have breached the ministerial code by not properly declaring his family's shareholding in a company that had won contracts with the NHS in Wales and "potential supplier" status for the NHS in England.
The prime minister's official spokesman said there had been no conflict of interest because Mr Hancock had no role in awarding the contracts and had consulted the top civil servant in his department before accepting the gifted shares.
But new revelations in The Sunday Times raise further questions for the health secretary, with the newspaper publishing emails from David Cameron to Matthew Gould, head of the digital wing of NHS England, in which the former prime minister claims Mr Hancock was "extremely positive" about making Greensill's salary advance service, Earnd, available to NHS staff.
The context of the comment, according to The Sunday Times, was an email in which Mr Cameron attempted to persuade Matthew Gould to assist Greensill in getting Earnd access to electronic staff records of NHS employees to make the system "much slicker".
Labour's shadow Cabinet Office minister, Rachel Reeves, described the reports as "appalling beyond belief".
"David Cameron wanted to profit off the NHS, and the health secretary and current Conservative government gave him an open door to do so," she said.
"At the height of the pandemic, when our NHS workers were risking their lives, there were some at the top of the Conservatives looking to enrich themselves.
"Tory sleaze is back and it is bigger than ever."
Sky News approached NHSX, which sets national NHS technology policy, for a comment.
An NHSX spokesperson said in a statement that it is "supportive of technology that can improve employee wellbeing and make it easier for nurses, doctors and other NHS staff to do their jobs, and when services are procured this is always done transparently and following the appropriate processes".
They added: "Greensill was one of many 'fintech' firms which approached NHSX to discuss their products as part of our 'innovation surgery' but we did not enter into any contract or partnership with them."
A spokesman for David Cameron added in a statement: "David Cameron's letter to Matthew Gould emphasised that Earnd was free for NHS employees and that there would never be any charge for the service to the NHS.
"It also made clear that an employee's data would never be sold.
"Earnd has explained that it never sought access, nor was it ever given access, to macro data, only data for those individual employees that opted in.
"As Mr Cameron made clear in his statement last weekend, he became an enthusiastic advocate for Earnd, which enabled employees to see and access their pay as they earn it, in real-time and, crucially, for free, with no charges or interest rates, rather than having to wait until the end of the month."