The UK’s business leaders are not, on the whole, committed Corbynites, but last autumn their political centre of gravity started to shift. At the CBI’s annual conference in November, the warmest applause went not to Theresa May but to her rival on the opposition benches. After the Labour leader’s speech, the measured reaction of one captain of industry – “These are great aims. But how will they be paid for?” – reflected the perhaps surprisingly pragmatic response of British business to the prospect of a socialist government.

Few corporations are keen on taxes or regulation, but all will welcome the state investing £250bn in infrastructure and research and development, as well as billions more on education. They are also grateful that Labour has maintained its position as the party of soft Brexit.

John McDonnell’s series of emollient conversations last year with City executives – his “cup of tea offensive” – seems to have worked.

But this morning Corbyn’s key ally presented a less rosy picture when he spoke at the World Economic Forum. Although he wanted guests there to know he’s a man they can do business with, he also made clear that they don’t have much of a choice. “Out there, beyond the Davos compound, many people feel the markets are rigged against them,” he told his audience. “There is an anger building that you have to deal with.” As he warned on Wednesday: “Change is coming either way.”

The shadow chancellor has been invited to Davos because the global elite know he has got a point. “Business … needs to have a societal tone,” admitted John McFarlane, chairman of both Barclays and financial services lobby group TheCityUK, last year. “Ordinary people have spoken out and they are finding it hard.” He concluded, in his interview with Reuters, that Labour’s confidently leftist general election campaign had been “bang on”.

You might think that the forces of global capital really should be a bit more consistently antagonistic towards a party “for the many, not the few”. But consider what motivates the people who were sitting in McDonnell’s Davos audience.

A minority of those who were there – the hedge fund types – are professionally obliged to focus not on grand political questions, but on short-term prospects. Even if they suspect their margins might feel a little pressure from Labour’s redistributive plans, they are principally concerned with identifying how they would make a profit in any likely scenario.

However, different concerns occupy the archetypical guest at the WEF, one of those who might happily chat with Bono and the Gateses in the hot tub after a long day of seminars. They hope a brief spell of social democracy will save capitalism from itself, just as it has several times in the past century.

McDonnell’s long-term goal of a democratic economy is very different to that of WEF ticket-holders, but evidently the conditions for a truce are promising, hence the invitation to Switzerland. The change in tone from business a few months ago was a sign that ideology and power were rearranging themselves.

‘Ordinary people have spoken out and they are finding it hard' John McFarlane, chairman of Barclays and TheCityUK

The save-capitalism-from-itself crowd hopes Labour and other leftists can cure some of globalisation’s pathologies, social and economic. Since the 1980s and 90s, privatisation has prevented the state interfering, as the free marketeers see it, in what is supposedly the realm of business: creating value.

But as has been elaborated by economist Mariana Mazzucato, the state often leads the way in incubating innovation. Many high-growth areas, from computing and the internet to biotech and nanotechnology, have been identified by the state, supported for years and even made commercially viable by it, long before venture capitalists or big corporations got involved.

Consequently, in the UK’s heavily privatised economy, growth and living standards have depended not on creating value but on merely extracting it, on borrowing from the oil producers of the Middle East and the manufacturers and industrialists of south and east Asia. This global imbalance precipitated and shaped the crash of 2007, and since then the Tories’ response has been to encourage more of the same, so that our economy is still overheated with private debt. Free market policies haven’t just made Britain violently unequal: they have made our economy unstable.

Labour’s manifesto last year offered a solution. Government borrowing will have to increase, but if the state pulls its weight as an investor and an entrepreneur, stimulates growth and helps to rebuild industry and manufacturing in the UK, Britain can become a value creator once more.

This is implicitly acknowledged when even mainstream Tory MPs such as Sajid Javid, Nick Boles and Tom Tugendhat demand an end to austerity or when May starts talking of her “industrial strategy”, a vaguely Keynesian phrase all but banned since 1979. Those Tories know Labour’s economic plans are not just popular: they provide a response beyond keeping calm and carrying on.

Few at Davos or in the City will have agreed with every word spoken by the shadow chancellor today, but they are pragmatists. After McDonnell met BlueBay Asset Management in November, the $57bn hedge fund cut its short positions against sterling in half. Previously, its managers had been betting against the pound, but they explained that they had liked what they heard from the shadow chancellor. Indeed, they publicly dismissed fears that if British voters put Labour into office currency speculators might sabotage sterling.

McDonnell’s appearance at the WEF confirmed not only that his solutions sound attractive far beyond his voter base, but also a more pragmatic message: the global elite knows he and Corbyn may enter government very soon, and that by 2022 they could well have been joined by a President Mélenchon and a President Sanders. McDonnell’s rivals at Westminster, and around the world, should be worried.

• Richard Power Sayeed is the author of a history of New Labour and Britain in the 1990s, 1997: The Future that Never Happened