An inquiry into Downing Street parties that could determine the fate of Boris Johnson’s premiership should be given greater independence from No 10, former civil servants and a union leader have warned. It comes amid concerns that the prime minister could veto the conclusions of an inquiry by Sue Gray if she recommends that he should be investigated under the ministerial code. Gray, a senior civil servant, was appointed last month to examine claims that Downing Street officials broke Covid rules by holding a series of parties and events during the pandemic. She replaced her line manager – the cabinet secretary, Simon Case – after it emerged that a Christmas quiz was alleged to have been held in his office. However, her inquiry has grown in gravity and potential impact amid calls for Johnson to step down following a public outcry over further party revelations. On Wednesday, Johnson gave a partial apology for attending a “bring your own booze” party in No 10’s garden on 20 May 2020. Keir Starmer, the Labour leader, accused Johnson of breaking the ministerial code by making misleading statements in a series of denials about parties at No 10. “That code says ministers who knowingly mislead parliament will be expected to offer their resignation,” Starmer told MPs. Afterwards, several Tory MPs privately said they would await the Gray findings and, if damning, call for their prime minister to quit. Gray, whose inquiry could conclude as early as next week, can recommend that Johnson has broken the ministerial code. The terms of reference for her inquiry state that “the conduct of ministers should follow the process set out in the ministerial code in the normal way”. However, Dave Penman, the head of the FDA union, which represents senior civil servants, said if Gray makes a recommendation for further inquiries under the ministerial code, Johnson still has the power to block it. “The prime minister himself gets to decide if he needs to be investigated under the ministerial code. No one else can make that decision and he has so far refused to give up this veto despite the recommendations from the committee for standards in public life to do so,” he said. Gray is running the inquiry from the Cabinet Office along with staff members from the propriety and ethics team. She previously headed the same team for six years, during which she ended the careers of three cabinet ministers and vetted the memoirs of ministers. Senior civil servants have expressed concern that the inquiry’s conclusions will be scrutinised by both Johnson and Case. Bob Kerslake, the former head of the civil service, said he had previously been happy for the inquiry to be run by Case but believed the latest revelations meant a retired judge should be asked to receive Gray’s findings. “Sue Gray is an immensely capable investigator but one has to recognise that two of the principal actors here – the PM and the cabinet secretary, effectively her bosses – are now deeply implicated in the inquiry. That is completely unprecedented. The findings could decide whether they stay in their jobs or not. “The latest revelations over the events of 20 May 2020 have raised real questions as to whether there should be another independent person involved – a retired judge, for example – who could then receive this report, rather than it being passed directly on to the prime minister and the cabinet secretary,” he said. Sir David Normington, who worked at the Home Office and oversaw public appointments, said Gray had been placed in a “very odd” position as the public waited for her verdict. “She’s in the middle of a political maelstrom at the moment, trying to establish the facts, and there’ll be a lot of pressure on her to conclude this investigation as quickly as possible,” he said. “She will be very aware that she has the reputations and possibly the careers of senior civil servants and possibly of the prime minister in her hands. That is a very difficult position to be in, however fair and fearless and rigorous you are.” A Cabinet Office spokesperson said they would not speculate on the inquiry.