Labour members and supporters face an awesome responsibility after the party’s worst defeat since 1935. In the coming weeks, the choice of its next leader lies in their hands. Their decision will shape the difficulty and length of Labour’s path to government and determine how effective an opposition it is in the coming years, when the government appears hellbent on delivering a damaging hard Brexit.

Britain is in desperate need of a Labour leader who will hold this government to account and who will learn the right lessons from the party’s failures. A six-week spell of hustings events kicked off in Liverpool, with the five leadership candidates setting out their pitches. What they say will reveal the extent to which they can speak hard truths to the left-leaning membership in a way that wins round their support rather than alienates them. One notable difference between this contest and those that have preceded it is the extent to which women dominate the field: a positive step for a party that has never elected a female leader.

The first test for candidates is the extent to which they are willing to speak the truth about why Labour lost so abysmally last month. Labour has only won three elections in the last 45 years and what drove those victories was Tony Blair’s ability to build and sustain a broad electoral coalition. That coalition has eluded Labour since 2005: election results since then show a steady decline in the party’s working-class support, which it once would have considered rock solid, and a drop in support from older voters and non-graduates.

Brexit put boosters under this disconnect between the party and its historic base. Voters were not clear about what the party stood for on Brexit: its fudged stance convinced too few. But there was no bulletproof Brexit stance Labour could have taken. If it had become the party of soft Brexit, it would probably have lost more votes to other Remain parties. Brexit was more salient an issue to Labour-leaning voters who voted Leave in 2016 than Conservative voters who voted Remain. Not enough Conservative Remainers could live with Jeremy Corbyn in Downing Street as the price of potentially averting Brexit. Too many Labour Leavers favoured Boris Johnson’s pledges on Brexit over a Labour government.

That is because of a failure of leadership. Even before the election campaign began, Corbyn was the least popular leader of the opposition for decades. Post-election polls suggest that his leadership was the biggest factor in turning off voters, undoubtedly buoyed by a distrust of him on national security issues and his monumental failures on antisemitism. Labour’s manifesto lacked credibility with voters, who justifiably did not believe they could have everything from free broadband to a four-day working week without paying in more, and the “many versus the few” framing of its campaign did not resonate with enough voters.

Facebook Twitter Pinterest ‘Even before the election campaign began, Jeremy Corbyn was the least popular leader of the opposition for decades.’ Photograph: Anadolu Agency/Anadolu Agency via Getty Images

This multifaceted nature of Labour’s defeat allows candidates disinclined to face up to hard truths to pick and choose their narratives to serve their interests. We have already seen that in this contest. Too few candidates have proved willing to acknowledge that last month’s result hardly shows an electorate ready to embrace a socialist policy platform; the more common refrain is that Labour just didn’t make the case well enough or that there was too much good policy for voters to take in. Rebecca Long-Bailey, one of the two frontrunners, has been too willing to blame the defeat on the party’s essential parliamentary opposition to a hard Brexit and media hostility, rather than its leadership or policies. Members must choose a candidate who has the bravery and leadership to front up to why Labour lost.

Beyond that, leadership candidates should be judged according to the extent they can build a broad coalition that unites Conservative-leaning swing voters, working-class voters who voted Labour all their life but who have switched away in recent years and younger voters angry about the raw deal they are getting on housing and pensions. That means not writing off particular areas of the country or particular groups of voters as evil Tories. It means choosing a leader who can connect based on the values that voters hold, rather than, as Corbyn did, starting from the perspective they are unfailingly right and lecturing voters who do not share their ideology on why they are wrong. It does not mean lumping 13 years of Labour government into “40 years of Thatcherism”, as one new Labour MP did last week, or labelling the pre-Corbyn Labour party as “Tory-lite” as Long-Bailey has done. What faster way to speed up Labour’s irrelevance than by telling the millions who voted Labour during these years that they might as well have voted Conservative?

Building a broad electoral coalition will also mean developing a different, credible policy platform that speaks to the big challenges facing the country, such as ageing, the climate crisis and the poor employment prospects many young people face. That will require prioritisation: free social care over free broadband, levelling up the lack of investment in young people who do not go to university, before scrapping a graduate contribution to higher education. It will require a leader who can combine strong parliamentary opposition to a Conservative hard Brexit, while unifying those who voted Remain and Leave in 2016 ahead of the next election.

Labour’s next leader faces a monumental task. The bar is high for would-be Labour prime ministers and Gordon Brown, Ed Miliband or Corbyn could not meet it. It is too early to tell which candidate has the ability, courage and integrity that makes them best placed to try to clear it in a few years’ time. But as this contest unfolds, it is incumbent on Labour members to choose wisely. The future of the country depends on it.