What self-respecting political leader would be seen in Davos? The World Economic Forum has become synonymous with sybaritic technocracy – champagne receptions, luxury chalets, £50 burgers and traffic jams of black limousines. David Cameron and George Osborne were in their element at these summits, sometimes staying to ski afterwards. But Rishi Sunak, a Goldman Sachs alumnus, has decided not to go this year, no doubt worried that his attendance would reinforce stereotypes he’s trying to dispel.

Sir Keir Starmer has no such inhibitions. He’s making his debut as a Davos Man this week, alongside Rachel Reeves, his shadow chancellor. He will attempt to look like a prime-minister-in-waiting on a panel with Mark Rutte, the Dutch Prime Minister, about ‘repowering the world’. Reeves will continue her quest to restore Labour’s reputation for fiscal discipline in a discussion on the question ‘Is the world in a debt spiral?’. ‘It’s ironic given the legacy of former Labour governments,’ snipes a government aide.

Labour and the Tories are happy with the arrangement. It allows them both to address their perceived weaknesses: Starmer as anti-business and Sunak as out of touch.

The Labour leader is on a mission to prove his economic competence – one of the two issues where he polls worse than Sunak. (The other is ‘works well with foreign leaders’: another reason to go to Davos.) Reeves and Starmer’s message at the summit will be ‘with Labour in government, Britain is open for business’.

Reeves, a former economist at the Bank of England, has been getting into her role as a City-friendly shadow chancellor for a while now, embarking on a time-intensive charm offensive with business leaders. ‘I was at a breakfast meeting she addressed recently,’ says one Tory peer. ‘And I hate to say it, but she was plausible. All too plausible.’ Her Davos double act with Starmer is meant to add to the sense of professionalism. One minister is worried that the tide has already turned: ‘It’s switched. The media have started paying a lot more attention and there is a buzz around them.’

Sunak is still recovering from previous disclosures about his wife’s non-dom status and his former possession of a US green card. Over the summer, some Tory MPs who supported Liz Truss complained that he wasn’t sufficiently committed to Britain and would be on the next flight back to California if he lost the leadership contest. (‘That’s not true,’ he joked to party activists. ‘The cheapest flight is on a Tuesday.’)

When Sunak entered Downing Street, it wasn’t even a matter of debate that he would avoid Davos. International Trade Secretary Kemi Badenoch is attending instead – but she, too, is sceptical of the summit and will avoid appearing on any panels. ‘The Prime Minister is focused on delivering for the British people here at home,’ says a Downing Street source. In other words, Davos is a waste of time. A government aide goes further: ‘There are much more pressing things than brushing shoulders with the world’s millionaires and billionaires.’ As a millionaire married to the daughter of a billionaire, Sunak would know.

MPs in the Red Wall tend to be the most critical of Sunak, arguing he is too smooth and lacks the cut-through that led Boris Johnson to win their seats in 2019. His itinerary in recent days – Leeds, Inverness – has helped to win some of them over. Workington MP Mark Jenkinson heralded his boss as ‘relentlessly focused on our issues here’, while ‘Sir Keir Starmer’s priorities clearly lie in Davos’. Sunak knows his only hope of turning around his party’s fortunes is by disproving public scepticism and delivering, in a way that his two predecessors struggled to.

But his problems are mounting, as the NHS teeters and unions prepare for more strikes. Sunak has been trying to come across as reasonable, not hardline, on the strikes. His ministers are under strict instructions always to appear the more responsible party and paint the unions as the wreckers. So far, public opinion is mixed as to who is to blame. The Minimum Service Bill – to ensure a certain proportion of workers keep working during strikes – now going through the Commons is viewed as a political success in the party, despite furious attacks from Labour. ‘The strike votes have been good for morale,’ says a senior Tory. ‘It’s useful in Red and Blue Wall seats where voters are sick of the lack of service on trains.’

A case in point can be found in the fact Jake Berry – a former cabinet minister, Johnson loyalist and serial rebel – shared a video to say he was voting for the bill. According to a YouGov poll, more than half of the electorate backs it. Labour’s campaign to attack the legislation is not being viewed with much concern in Conservative Campaign Headquarters.

However, with the biggest education union voting to strike and nurses’ strikes showing little sign of abating, some ministers are worried that the reasonableness argument could backfire, and Sunak could look out of sync with the national mood. While there have been efforts to reduce the disruption so far (the military handled passport control with astonishing speed), if children miss school, meaning parents have to take time off work, there will be a noticeable hit on the economy.

The nurses command the most public support. ‘The Prime Minister needs to end the nurse dispute as soon as possible,’ says a senior government figure worried about the optics of a protracted row. Money could be on the table, but ministers are reluctant to do anything that could raise the tax burden. A hint of how it might be done can be found in the language the Health Secretary used in a letter to health unions. Steve Barclay talked of looking for ‘productivity and other contract flexibilities and efficiencies’ that would allow the government to revise ‘our evidence’ to the pay review body.

Sunak and Starmer both have weaknesses they need to correct. But as Starmer parades around the stage at Davos, it is Sunak who’s under the greater pressure to show he can move up a gear.