Chuka Umunna’s description of the Labour party “behaving like a petulant child who has been told you can’t have the sweeties in the sweet shop” in the summer of 2015 was a somewhat crude summation of what became the prevailing attitude of Jeremy Corbyn’s internal opponents. While they would happily accept that thumbing their noses at the public for rejecting Labour was counterproductive, they never applied the same logic to their own party’s membership, too often regarding them as a delusional, ideologically crazed cult.

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In this leadership election, the three remaining candidates understand that this is a self-defeating strategy. They recognise that Labour’s membership has two priorities: to preserve the core policies of the Jeremy Corbyn era, and to defeat the Tories to secure power. Members see no contradiction between these two aims, and indeed polls support that view.

The question haunting the race is: are the candidates genuinely committed to those policies, or are they saying what members wish to hear, only to pivot rightwards when the crown is secured? Those close to Lisa Nandy and Rebecca Long-Bailey’s campaigns speak with frustration at Keir Starmer’s adoption of a “classic frontrunner strategy”: of playing it safe, saying little and avoiding any excessive scrutiny. But last week Starmer’s team released “10 pledges” which commit him to maintaining core policies such as hiking tax on the top 5% and big business, public ownership, tuition fees, reversing anti-union laws and opposing illegal wars.

After Starmer was interviewed in a room that boasted a set of drapes familiar to the shadow chancellor, John McDonnell quipped it was “Continuity McDonnell. I am pleased that the leadership candidates are largely following my policies but replicating my curtains as well demonstrates total hegemony.” The commitments provoked pushback, both publicly from centrist commentators and privately from some of Starmer’s backers. The attitude towards Starmer from the right of the parliamentary Labour party ranges from goodwill – partly relief at the Corbyn project facing internal defeat – to deep cynicism, which has only been heightened by the pledges.

Starmer’s team are emphatic that the pledges are both an attempt to reassure members and an authentic expression of his politics. But while they emphasise a breadth of support – ranging from the Old Labour right to two-time Corbyn voters – that could forge some desperately needed unity, it does raise questions about whether this is an unwieldy coalition. Someone will surely have to be disappointed: the question is, who, and how quickly? Starmer’s opponents argue that while his support is broad, it is also soft and lacking enthusiasm. There is also exasperation from the rival camps that while the two women in the race are being criticised for their unabashed support for trans rights, the sole man isn’t facing detailed scrutiny on the issue.

While Starmer’s team believe there is a general consensus on policy within the party, the Labour right may not be so easily disregarded. Much depends on who Starmer appoints to his shadow cabinet, which remains entirely unclear. While his campaign emphasises that he would appoint a shadow chancellor in accordance with his own views – pointing to the departure of Sajid Javid as evidence of what happens when the top two posts are not working as one – the left fear the appointment of someone like Yvette Cooper. That would instantly signal a return to technocratic Brownism and a strong departure from existing policies. If Starmer triumphs, as is likely, the left will undoubtedly treat the 10 pledges as sacred red lines the leadership cannot cross. If a rightward shift takes place, it would be self-defeating, leaving the new leader looking weak, unprincipled and cynical.

Nandy started her campaign with a strong set of media performances and is the only candidate who held out against a second referendum. The message her campaign has been keen to promote is of not tacking left or right, of avoiding a tokenistic shopping lists of policies, and of encouraging a sort of grassroots participation that her campaign believes Corbyn did not pull off effectively. But she raised considerable hackles on Newsnight’s hustings when she claimed Labour had failed to promote investment in buses – it was in fact a key manifesto commitment – and spoke of the party promising “to nationalise everything”, then later raising her hand to support public ownership. Her rival teams viewed this as an attempt to fill the space vacated by Jess Phillips and to peel off Starmer supporters disillusioned by his commitment to core Corbyn policies. Nandy’s allies rebut this – protesting that she is firmly of the left, just wishing to make radical policies workable. None of that makes it clear what her manifesto would look like.

Play Video 1:50 Labour leadership contest: Starmer, Nandy and Long-Bailey in TV debate – video

Long-Bailey’s team are acutely aware that it’s the middle third of the Labour membership they need to persuade: those who backed Corbyn, who are traumatised by defeat and have been persuaded by Starmer’s camp that he is more electable. Their task is threefold: to present Long-Bailey as the most trustworthy custodian of Labour’s policies, pointing to her work on the green new deal; to rebut claims she lacks charisma, sharing clips of her being relatable and jokey in interview clips and rallies; and to present her as well placed to win back Labour’s “red wall” seats because she was someone who wasn’t an architect of the party’s second referendum policy.

The latter is a particular challenge: most Labour members remain convinced the party was correct to shift on Brexit. With a hung parliament no longer an issue, Long-Bailey’s campaign believes the focus must be on building a strong movement in the country, particularly in communities that voted leave. Despite unfair claims that she simply represents “continuity Corbynism”, Long-Bailey has developed a clear critique of what went wrong in the election, not least the lack of a clear vision or narrative. Her challenge remains persuading Corbyn voters who have defected to Starmer that her leadership would sufficiently break with the mistakes of the past; so far, she has not succeeded in doing so.

It may well be that the legacy of Corbynism is a lasting shift towards economic radicalism in the Labour party. But the durability of those policies is not guaranteed, and if the Labour left is on the eve of losing power, its new role will be to organise to defend them. Long-Bailey’s campaign director, Jon Lansman, founded Momentum in the knowledge that it would be needed when the left no longer occupied the Labour leader’s office. That idea may soon be tested.

• Owen Jones is a Guardian columnist