The former Conservative leadership contender Jeremy Hunt has suggested he could run for the top job before the 2024 election as he warned Boris Johnson he had “a big mountain to climb” to win another term. Amid the fallout from the Partygate scandal and after bruising losses in last week’s local elections, Hunt told the Times Magazine it was not the “right time” for a leadership change due to the war in Ukraine. “But I would be very open with you that I don’t rule out a return in the future,” he added. Speaking to Times Radio, Hunt said the “setbacks” the party suffered in the local elections were not only “midterm blues” but reflected the cost-of-living crisis. “To win an election, the Conservative party has to promise a well-funded NHS and the prospect of tax cuts. If we make people choose between one or the other, we’re not going to win the election,” he said. “I do think that we would be wrong to say that the setbacks the Conservative party have are just midterm blues, and there’s a big mountain to climb to win the next election.” Hunt, a former foreign and health secretary, came second to Johnson in the 2019 Conservative leadership contest, having secured one-third of the vote. He stepped down as foreign secretary and turned down an offer to be defence secretary. Returning to the backbenches, Hunt became chair of the health and social care select committee. He was frequently critical of the government’s approach to the Covid-19 pandemic. This week, it was announced the Metropolitan police had made about 50 further fixed-penalty notice referrals as part of its investigation into possible lockdown-breaking parties in Downing Street and across Whitehall. It brought the number of fines to more than 100 – with Johnson, his wife, Carrie, and the chancellor, Rishi Sunak, receiving fixed-penalty notices in April over a birthday party held for the prime minister in No 10’s cabinet room in June 2020. In last week’s local elections, the Conservatives suffered a net loss of 487 seats, while Labour gained 108 and the Liberal Democrats 223. Commentators have warned the results show Johnson’s majority could be in jeopardy at the next general election. Ministers dodged questions on whether they still had faith in the PM when asked about the latest development as they emerged from a cabinet away day in Stoke-on-Trent. The home secretary, Priti Patel, failed to say whether or not she still supported Johnson, while the health secretary, Sajid Javid, also chose not to answer when asked why the PM would not resign, despite Keir Starmer’s promise to do so if he is handed a fixed-penalty notice over similar allegations. The Brexit opportunities minister, Jacob Rees-Mogg, the culture secretary, Nadine Dorries, and the education secretary, Nadhim Zahawi, have all backed the prime minister. There have been ongoing calls for Johnson to resign over the saga from opposition MPs, as well as his own backbenches, but he has said repeatedly he is determined to get on with the job.