When a Labour politician or aide stops to chat in the corridors of parliament these days, they only have one question: which leadership candidate would the Tories fear most?

The government majority of 80 means it would be hard for even the most talented Labour leader to land a House of Commons victory in the coming years, yet he or she would still have the potential to change the dynamic of this parliament — and disrupt the Tories’ hope for the 2024 election.

Right now the leadership candidates are focusing not on hurting the Tories but on wooing the MPs, trade unions and members whose support they need to win. It’s the Labour membership who will have the final say, but in order to reach this stage of the contest each candidate must first secure the backing of at least 21 MPs and then the support of either 5 per cent of local parties or three nominations from unions and affiliate groups.

Of the six candidates in the race, Emily Thornberry, Lisa Nandy and Clive Lewis look like they might struggle to clear this bar. Thornberry has done little to ingratiate herself with parliamentary colleagues, while Clive Lewis and Lisa Nandy are fishing in the same pool. When it comes to soft-left and Corbynite MPs, one leadership campaign calculates there are 70 — and a lot of these are already behind Rebecca Long Bailey.

Jess Phillips is seen as having a good chance of reaching the membership vote. However, her problem comes once she gets there. Since she entered parliament, Phillips has emerged as a strong media performer. But she has been openly critical of Corbyn — once telling his ally Diane Abbott to ‘fuck off’. Such behaviour isn’t popular with a membership still broadly loyal to the departing leader.

‘Jess can win the leadership,’ says a party insider. ‘It’s just to do that she needs to get 130,000 new members to join.’ Phillips’s supporters point to Jeremy Corbyn as proof that’s possible; in 2015 an insurgency of new members took him to victory. They hope to replicate that, but from the centre.

The window to do this is tight. The deadline for new members is 20 January, while registered supporters have 48 hours from 14-16 January to secure a vote by paying £25 for the pleasure. But it’s worth remembering that in 2015 Corbyn led among every section of the electoral college, rather than just new members.

The prospect of Phillips as Labour leader receives a mixed reaction among senior Tories. Her policy ideas have been lacking so far and she left open the possibility that Labour could campaign for the UK to rejoin the EU, a plan which would delight No. 10.

But some Tories view her as high-risk. Phillips has frequently criticised Johnson over his personal life. Even if she didn’t lead her party back to power, the worry is she could cause the Prime Minister severe damage along the way.

Long Bailey is the candidate the Tories would be most relaxed about winning. The shadow business secretary is the closest thing to a Corbyn continuity candidate. In an interview this week she awarded him ‘ten out of ten’ when asked to rate his time as leader. She not only still supports Labour’s 2019 manifesto, but has said that she was proud to have contributed to it. Among the parliamentary Labour party, this is not a popular pitch. ‘Anyone but RLB,’ bemoans one MP.

But despite a shaky start to her campaign which saw other Corbynites such as Ian Lavery consider throwing their hat in the ring, Long Bailey is well placed in the contest. She is likely to win the support of several of the unions and the pro-Corbyn grassroots group Momentum. Rival leadership teams worry that this would give her a clear advantage for targeting voters.

The candidate who is emerging as the favourite is shadow Brexit secretary Keir Starmer. He’s on course to receive the most MP nominations and a YouGov poll suggested he was heading for a comfortable victory. His campaign has so far been the slickest. In his launch video, the former human rights lawyer used his legal record to paint himself as a champion of the left, on the side of miners and poll tax protesters. It included footage of him embracing Corbyn. So effective was it that some of Starmer’s more centrist supporters have begun to worry that they may have misjudged him.

Ministers have started to discuss how best to attack Starmer should he get in. One argues that they should pitch him as a north London establishment figure not in tune with the people. He helped convince Corbyn to support a second referendum — which boosted the Tories in former Labour Leave heartlands. But even Starmer sceptics admit that he is more competent than Corbyn. The PM is not a details man, and Starmer’s precision could make things tricky for him at the despatch box.

As of yet, no candidate has struck fear into the heart of the No. 10 operation. However, there’s time for things to change before the winner is announced in April. After all, just a few months ago the Tories were worrying that they were facing years in the wilderness. In the election, the Tories defeated Corbyn, but Corbynism is not yet dead. In the results post-mortem examination, Tory election strategist Isaac Levido warned ministers that the Conservatives had not yet won the domestic policy argument. In fact, after the Labour manifesto launch — announcing a four-day working week and mass nationalisation — the Tories’ private polling of 120 marginal seats suggested the gap between the two parties had narrowed to four points.

A strong communicator leading the depleted party could still present a threat to the government. Notably, shadow education secretary Angela Rayner had such a successful launch for her bid for the deputy leadership that attendees couldn’t help but ask why she wasn’t running for the top job instead of her flatmate Long Bailey. Rayner declared that it was ‘win or die’, and impressed with her claim that she was a socialist but not a Corbynite.

And even if the next Labour leader flops, there’s still potential for the party to bring in a more formidable candidate before the next election.