There is a group of organisations in this country whose most senior roles are almost exclusively the preserve of middle-aged white men. These people do not seem terribly interested in the future, even though it poses grave threats to them and what remains of their power. Indeed, as the economy is endlessly disrupted and transformed, it appears their instinctive response is to bury their heads in the sand.

Though it does not bring me any great joy to say so, these are among the basic facts of 21st-century British trade unionism. Serially weakened by deindustrialisation and kicked around for the best part of 40 years, it is perhaps a miracle that the unions still have 6.2 million members. The work of representation, education and occasional mobilisation that their members continue to do is vital. For all that even leftwing people now seem to be questioning unions’ role within the Labour party, it is entirely right that some of the biggest unions have an organised means of political representation as a counterbalance to the infinite clout of capital. But that is not the whole story, and it is time some glaring failures were talked about in the open.

The big unions can appear to be just waiting for a Labour government to come along and somehow make things alright

Survey the general secretaries of Unite, the GMB, the giant public sector union Unison, the Communication Workers Union and the shopworkers’ union Usdaw – who collectively dominate Labour’s union-based structures – and you will see not a single female or non-white face. The same goes for the transport workers’ union the RMT and the public servants’ union the PCS. Frances O’Grady brilliantly does the difficult job of speaking for the entire union movement as general secretary of the TUC; Mary Bousted is a formidable joint general secretary of the newly formed National Education Union; and the University and College Union’s noble fight to protect its members’ pensions is led by Sally Hunt. About 55% of union members are women. But it surely says something that in living memory the only female trade union leader to have got close to being a presence in the wider culture was the late Brenda Dean, the general secretary of the print union Sogat and key voice in a seismic battle with Rupert Murdoch back in the mid-1980s. She died last week, and her passing has a very topical poignancy.

Last week, I spoke to a female staff member at a big union who sees at first hand how unions too often stifle potential. “If you make a request for flexible working, it almost feels as if you’re asking for a favour; you start to feel like you’re doing something wrong,” she said. I have also recently heard the story of a female union official who was granted flexible arrangements to look after children – but only on the condition that she was demoted. Meanwhile, the men who can put the hours in continue to rise to climb the ladder: a journey that will usually end with a comfortable salary and a long spell at the top.

A protest in central London against proposed changes to lecturers’ pensions. Photograph: Wiktor Szymanowicz/Barcroft Images

Three-quarters of Unison members are women. But insiders talk about an already bad situation that is getting worse. “Women are being replaced by men: the heads of regions are a good example,” one insider says. She goes on: “If you visit Unison’s HQ, you’ll have no idea most of our members are women. Women are tacked on to what the union does. They’re not at the heart of it.” In the wider union movement, needless to say, such grim imbalances are not just manifested in matters of gender: in 1992, when Bill Morris began a 11-year stretch as general secretary of the then Transport and General Workers’ Union (since folded into Unite), he became the first person of colour to lead a major UK trade union. As things stand, he remains the last.

The unions’ systems of membership still tend to revolve around a two-tier model split between “full time” and “part time”, and their basic unit of organisation is a workplace with a union rep. How this is meant to fit with working lives that can flip across such categories on a daily basis, and through offices and factories at speed, remains a mystery. I have spoken endlessly to trade unionists who want to give serious thought to how to do things differently: one idea that often comes up is of a lifetime individual membership that could be instantly reconfigured as people move into work, then out, and then in again, allowing them to make the most of different kinds of collective representation and personal benefits.

But such things are still more the subject of tentative conversations after office hours than anything more meaningful. Is this perhaps because the women, young workers and people of colour who tend to work in the more precarious parts of the economy are too often locked out of many of the big unions’ upper tiers?

Occasionally, you see signs of improvement. There are people within the big unions who do the hard work of taking trade unionism to people and places from which it is too often shut out: the GMB organisers who make it their business to recruit people working for supermarkets, courier companies, and outsourced hospital cleaning operators; the Unite activists who have talked to me about setting up credit unions and unionising call centres.

A bit further down the union hierarchy, there are the Bakers, Food and Allied Workers’ Union officials who worked with McDonald’s workers on a historic strike at two outlets that was followed by a nationwide pay rise, and the people from the media and entertainment Bectu who have devoted their energy to a long, grinding fight with the Picturehouse cinemas chain over pay and basic rights. However, across the unions as whole, unfortunately, far too little effort is going into developing these examples into anything that might capture the public imagination and begin to change some of the most iniquitous features of modern work.

Some radically different ideas are taking shape, thanks to a new breed of small, nitty-gritty organisations that work at the frontiers of precarious employment, and often have backstories involving frustration with the big unions’ lumbering ways. The Independent Workers Union of Great Britain not only did immense work winning improved rights to pensions and holiday and sick pay for cleaners at the University of London – a fight that goes on – it also miraculously secured a pay rise averaging 25% for bike couriers in five workplaces across London. The ambitiously named United Voices of the World has been central to a successful battle to bring cleaning jobs at the London School of Economics back in house. And the Cleaners and Allied Independent Workers Union recently won a guarantee of the London living wage for outsourced cleaners at the Nike Town store at Oxford Circus in London.

They may collectively have no more than a couple of thousand members, but these unions’ operations are fast, loud, and agile, and the faces of the people who keep everything together are admirably diverse. By contrast, the big unions can appear to be just waiting for a Labour government to come along and somehow make things alright. Is the work simply beyond them of reinventing their movement for new times so as to renew its liberating purpose? Are they holding back for fear of threats to their power? These questions require attention, before an iron rule kicks in: that complacency usually invites the slow sunset of irrelevance.

• John Harris is a Guardian columnist. He won political commentator of the year at the Society of Editors’ 2018 Press Awards