'You end in the grotesque chaos of a Labour council – a Labour council - hiring taxis to scuttle round a city handing out redundancy notices to its own workers.' One of Neil Kinnock's most famous and admirable moments was when he turned on the Militant tendency in his party from the stage at the 1985 Labour conference in Bournemouth. When he reached this section in the speech, he was heckled from the floor by Derek Hatton, the deputy leader of Liverpool Council, who called him a 'liar' for his attack on Liverpool council's conduct. Kinnock then addressed Hatton directly, saying: 'I'm telling you, and you'll listen - you can't play politics with people's jobs and with people's services or with their homes.' Militant was later found to be in breach of the Labour Party constitution, and Hatton was expelled in 1986. Most who entered government with Labour in 1997 felt Kinnock's confrontation with the hard left paved the way for the party's return to power in the ensuing decade. That speech has become iconic in Labour circles, with MPs quoting 'a Labour council - a Labour council' to one another in their best approximation of a Welsh valleys accent.

If the polls are to be believed, the Labour Party is going to be making a choice between a continuity Corbyn candidate in the form of Rebecca Long-Bailey, or a candidate who rejects that sort of politics to a greater or lesser extent. If the polls are to believed, it's most likely Keir Starmer who'll take on the job of being Labour's next Kinnock, trying to take the party away from even worse electoral irrelevance under the hard left and reminding its membership that its aim is to form a government again one day.

Kinnock, of course, had been expected to win in 1992, but he still gained 42 seats for Labour and paved the way for the party's landslide victory in 1997. No-one is currently expecting Labour to come anywhere near victory in the next election, and so the bar is much lower for whoever becomes leader.

The bar in this contest also seems lower when it comes to how a new leader would deal with the deep factional divisions in the Labour Party. The main talk over the past few weeks has been of unity and bringing the party back together. But today there is a party-within-a-party in the form of Momentum, which has had a number of hard left figures from the 80s, including many believed to have been members of Militant, in it from the very start, and staff at the very top of the party who many MPs do not consider to be Labour at all, such as Seumas Milne. And yet so far there has been very little discussion of how the next Labour leader will deal with what many feel has been a takeover by the hard left. All the candidates have made clear that they would have no tolerance of anti-Semitism and that Jeremy Corbyn should have done much more to stamp it out in the party. While this is the most pressing confrontation that needs to happen, it is separate from the matter of whether Labour plans to make itself electable again. When it comes to whether they'll boot out the hard left, the candidates are rather more ambiguous.

Starmer in particular is pitching himself as the 'unity candidate', pointedly hiring campaign team members from both sides of the party, from ex-Corbyn staffers Simon Fletcher and Kat Fletcher to former Liz Kendall campaign staffer Morgan McSweeney. He has said that while he wants to win back the traditional Labour voters who deserted the party in December, he also thinks Corbyn was 'right' to position Labour in the way he did, telling his launch event that 'we are not going to trash the last Labour government, but nor are we going to trash the last four years - there have been very many important moves'. He has clearly decided that the best way to win is to be neither hot nor cold.

Winning the leadership election is one thing. But does that mean he'll run the party in the same way, eschewing a Kinnock moment where he confronts those who have been taking the party in a direction contrary to its values? His supporters don't seem to have much appetite for that, at least. 'A Kinnock moment?' says one. 'I doubt that. His first focus would be to kick out anyone with any sign of anti-Semitism, that would be his first priority in terms of discipline and fresh standards. But I think he would be more inclined to use the force of argument than expulsion action.' Another says that his aim is to 'reunite what is a broad church against those who want it not to be a broad church', adding that the most important task for the new leader will be to ensure that the party has a 'reset' throughout its structures so that the hard left lose their stranglehold on the ruling National Executive Committee, for instance.

His backers do, though, expect him not just to take a harder line on policies like mandatory reselection, which meant many MPs spent last summer working on their local party membership rather than preparing for a general election, but also on bullying of colleagues. Corbyn pointedly refused to speak up for MPs who were being badly-treated by sections of the membership, including when the abuse had an anti-Semitic element. Starmer's backers expect that to change overnight if he wins.

I understand that Ed Miliband, who is backing Starmer for leader, has also advised him not to repeat Miliband's own attempt to try to keep everyone on side the whole time. One of the lessons the former Labour leader seems to have learned from his time in frontline politics is that appeasing one extreme or the other of a party only comes back to bite you, as those extreme elements then expect you to cave on other matters further down the line. Miliband declined to comment on this when I approached him.

MPs behind the other campaigns to elect Lisa Nandy, Jess Phillips and Emily Thornberry have a different take on the need for a Kinnock moment, though. Most agree that the next leader does need to do something to show that they just aren't going to tolerate the hard left any more, and that they'll need to do it early. 'Whoever becomes leader in April will have a very short window to say that you are either with me or against me,' says one Thornberry supporter. A Nandy backer agrees: 'This has got to be confronted at the right moment and a new leader will have to cash in some of the political capital that comes with winning. And to get the party elected again, that will mean taking some action to deal with some of the people who aren't interested in winning elections.' Anna Turley, who lost her Redcar seat in December, wrote a furious piece recently deriding the vogue for talking once again about 'unity'. She wrote: '..if unity is to be prized above all else - above asking the difficult questions and making the necessary compromises, expelling racist members, tackling abusive behaviour and bullying in local parties, speaking truth to power (or, indeed, to members) or being honest about why we lost and what it will take to win – then the Labour party is doomed to slip back to 2014: heartily applauding our internal comradeship, but ultimately failing the public test for which we were created.' Turley hasn't said who she is backing yet, but it won't be Long-Bailey.

Thornberry only just scraped over the line for MP/MEP nominations, but a couple chose to back her following her performance at the parliamentary party hustings, where they felt she had the strongest line on booting out anti-Semites. 'One of the reasons I am backing her is I think she is capable of that magic moment where she stands up to people,' says one MP. 'She's got the guts to do it, to take this on. That Neil Kinnock moment has absolutely got to happen.'

Some centrist MPs were put off Thornberry because she served in Corbyn's shadow cabinet and was so happy to defend him. Others have been put off because since the election, she has been so happy to denounce him. She may find the same problem in the wider party membership, with activists taking against her either because she has at one stage been loyal to Corbyn or because she has been disloyal. Phillips doesn't have the same ambiguity: her struggle is more about explaining what she really meant when she said she would knife the Labour leader 'in the front'. Despite her insistence that she was trying to say she wouldn't be one of the MPs who'd gossip behind Corbyn's back without airing her concerns to his face, she may find that the hard left is able to dodge her criticism because of those comments, made very early on in her time as an MP. But her supporters think her blunt tone is precisely what is needed for that Kinnock moment. One adds: 'She obviously will do something like Kinnock. Let me put it this way: would Keir have Richard Burgon, Ian Lavery and Jon Trickett in his shadow cabinet? Because Jess won't.'

You're unlikely to hear much from the candidates themselves during this contest about how they'd deal with the hard left. But they will have been thinking about it all the same, because whoever does become leader does need to answer the question: is your main aim really to reunite the party, or to make it electable?