The government’s announcement that it will go ahead with a third runway at Heathrow seems to have unlocked an array of demons. It has also created some unlikely alliances. Zac Goldsmith, the pro-Brexit mayoral candidate whose campaign was widely condemned as racist, is seeking to re-invent himself as an environmental champion, campaigning alongside fellow Heathrow MP John McDonnell. And the Richmond byelection which he is triggering could yet become a test case for Labour’s progressive alliance enthusiasts.

But perhaps the most significant position is that of the major unions. To the shock of many less seasoned activists on the left, Unite, the largest trade union in the UK and a consistent supporter of Corbyn’s leadership, has loudly called on the government to “be bold and build” the new runway, even now urging it to accelerate the process. Far from being a revelation, Unite’s position on Heathrow is longstanding – and it points to the lasting power and influence of an establishment trade unionism.

In August, the TUC co-ordinated a joint statement from five unions, urging the government to go ahead with the third runway. Like the rest of the unions’ lobbying efforts, it was coordinated with other pro-expansion stakeholders like the CBI, and it could just as easily have been authored by the business lobby. Heathrow expansion will, it says, “deliver at least £147bn to UK GDP and 70,000 new jobs”. “Trade unions and their members”, said Frances O’Grady, “stand ready to work to help the government successfully deliver this next major national infrastructure project”.

The logic that drives unions to support projects like Heathrow expansion – and which drives the GMB union to support fracking and Trident renewal – is grounded in a model of trade unionism which focuses not on transforming the workplace, but on the narrowly-defined interests of workers – job creation, economic growth and a larger share of the pie. It views the trade union movement not as merely antagonistic to employers, but as a responsible lobbying partner for business and industry, and as a means of mediating workers’ demands in a way that is steady and acceptable to the state and the economic system. This model, and the politics that accompanied it, is why, historically, trade unions were a conservative influence on Labour’s internal politics.

Nothing could be more at odds with the political, environmental and economic realities of the 21st century. It is not in the interests of workers or ordinary people to live on a planet which is slowly becoming uninhabitable. To avoid catastrophic global warming, we need to leave the vast majority of fossil fuels in the ground – that probably means shrinking the aviation industry, not expanding Heathrow’s passenger capacity by 70 per cent. All of this is implicitly recognised by Jeremy Corbyn’s environmental and industrial strategy, which aims to create a million new jobs and build a million new homes while switching to renewables and democratising the energy industry.

The gap between Corbyn’s policies and the policies of many major trade unions tells us something deeper about the challenges facing the left. If Corbynism is an unfinished revolution in the Labour Party machine, it is one which has barely started in the wider labour movement.

The gradual leftward shift in many unions’ political allegiances has broadened the alliance around Corbyn and given him strength in numbers and resources, but it is often as much about internal union politics as it is a deep conviction for what Corbyn represents. Unison general secretary Dave Prentis did back Corbyn’s re-election following a ballot of members, but is hardly a left-winger, and the union’s votes on Labour’s NEC are not safely aligned to the left.

The political radicalisation of the unions has been matched, if anything, by a decline in coordinated industrial action. The national strategy that fuelled the anti-austerity movement in 2011 and 2012 is only a memory. The democratic and organising culture in many unions, too, remains bureaucratic and opaque. Trade unions have played a key role in Corbyn’s coalition, but without a significant shift in their internal culture and a shift away from their role as respectable partners of industry, they could easily scupper the project as well.

The expansion of Heathrow airport is a step backwards for the future of the planet and the interests of ordinary people – and yet, if it happens at all, it will have been made possible by the concerted efforts of key trade unions. This is not an aberration but a reminder that, despite their rhetorical flourishes in support of Corbyn, Britain’s trade unions are also in need of change. Any project that aims to transform the Labour party and wider society must also aim to transform the whole of the labour movement – from the shop floor to the corridors of power.