At a Labour away day at ­Unison’s headquarters in central London on 20 March, the trade union’s general secretary, Dave Prentis, provided the calm before the storm of a shadow cabinet slugfest. Prentis, who leads an organisation representing 1.3 million public-service workers, achieved a feat that has evaded Labour’s struggling leader. He unified, if temporarily, Jeremy Corbyn’s squabbling frontbenchers.

For 35 minutes the shadow cabinet nodded as Prentis itemised the destructive impact of Tory austerity: the worsening wages, the cuts to public services, the suffering heaped disproportionately on women. He then explained why Labour should champion carers as well as the cared.

But it all went downhill as soon as Prentis left the room. A shadow cabinet member who was present told me that some Labour heavyweights had refused to play Corbyn’s chosen parlour game, which asked them to name their three most pressing priorities.

That Unison hosted this event illustrates how deeply trade unions are embedded in the Labour Party. The political and industrial wings of the labour movement are bound together organisationally, financially and culturally, in pursuit of a better deal for working Britons.

Talk privately to trade union general secretaries – as I have been doing for nearly three decades, during which time, more often than not, the Conservative Party has been in power – and most will freely admit that the biggest single improvement to the lives of the toilers and strivers they represent would be a Labour government. With Labour in office, doors in Whitehall open to the union movement. There is also the promise of broader benefits, such as better employment law, a real living wage, higher NHS spending, council house-building, and so on – all policies promised by the party now marooned in opposition.

Given that Jeremy Corbyn looks unlikely ever to make it into 10 Downing Street, why do the unions tolerate or, in some cases, continue to support his leadership? Trade unionists are by nature pragmatic dealmakers and, in private, nearly all admit that Corbyn’s leadership isn’t working. The disagreement, however, is over what to do next. The easy option is to do nothing, yet the first stirrings of rebellion can be heard.

Most trade unions were swept along by the 2015 groundswell that put Corbyn in charge. The majority stuck with him in 2016 after the attempted coup by Labour MPs. Prentis views Corbyn as a friend, the Labour leader having won goodwill by appearing on picket lines for decades at the drop of a Lenin cap. In policy terms, Corbyn was much closer to Unison’s positions than his rivals for the leadership were.

But after Labour lost the Copeland by-election to the Conservative Party in February, the tone shifted. “The blame for these results,” Prentis said afterwards, “does not lie solely with Jeremy Corbyn, but he must take responsibility for what happens next.”

The moment to remove Corbyn is “not now”, many trade unionists say. This mood is best articulated by the left-wing Labour loyalist Mick Whelan, the general secretary of the Aslef train drivers’ union and chair of the Trade Union and Labour Party Liaison Organisation, which co-ordinates 14 affiliates representing nearly three million members. Whelan, who will probably win one of the union seats on the party’s National Executive Committee later this year, says: “The real belief seems to be that yet another leadership election would be destructive and counterproductive. ‘No outstanding alternative’ is also a recurring theme with most people I talk to.”

Float the names of potential Labour leaders with general secretaries over a pint (such as Keir Starmer, Lisa Nandy, Clive Lewis, Angela Rayner, Rebecca Long-Bailey, Emily Thornberry, Yvette Cooper, Jonathan Ashworth, Louise Haigh and Tom Watson) and there is no consensus. The absence of a challenger is Corbyn’s greatest advantage.

Most union initiatives are co-ordinated by a “big four” of general secretaries: Unite’s Len McCluskey, the GMB’s Tim Roache, Dave Ward of the Communication Workers Union (CWU) and Unison’s Prentis. Corbyn has fractured their unity. Roache and the GMB, which sat out the 2015 leadership contest, plumped for Owen Smith last year after a survey of its members found that most of them wanted a change at the top. I understand that this quartet, who speak for 3.5 million workers, haven’t convened recently, though they still speak regularly.

Matt Wrack, the Corbyn-supporting general secretary of the Fire Brigades Union, which restored formal relations with Labour in 2015 after severing ties during the Blair era, believes that rebellious MPs are to blame. Wrack rejoined the party, a quarter-century after being expelled over his ties to Militant.

“There is an unending attempt to undermine Corbyn and, regrettably, much of it comes from within the Parliamentary Labour Party,” he says. “As in any organisation, there are clearly improvements that can be made but it is clear that a defeat of Corbyn or his removal by any means would mean a huge step backwards.”

The trade unionist best placed to pull the rug from under Comrade Corbyn is McCluskey. The Unite leader is distracted by a campaign to secure his re-election as general secretary (voting has begun and the result will be announced on 28 April). He is currently occupied ducking the mud thrown by his main challenger, Gerard Coyne, an old West Midlands mucker of Labour’s deputy leader, Tom Watson. Watson has fallen out with McCluskey since the not-so-distant days when they shared a London flat (the origins of their animosity are unclear but Corbyn is now at the heart of it). Yet “Red Len” is a far more nuanced figure than the stereotype portrayed by the Tory tabloids.

In 2015, there were whispers that McCluskey favoured Andy Burnham. Yet the latter’s bewildering policy positions gave the Unite leader no chance of ­persuading his leftist executive to back anyone but Corbyn. On 26 March this year, McCluskey repeated on BBC Radio 5 Live what he had previously told me was his “15-month goal” for Corbyn to improve matters. “I hope Jeremy can rectify the unfair image the media have placed upon him,” he said to me. “We all have to do what we can and see how the next 15 months unfold.”

The threat is implicit rather than explicit. Nobody in the union movement under­estimates the personal cost to McCluskey if he turns on Corbyn, particularly given that the Unite boss’s close friend Karie Murphy is the Labour leader’s office manager. The comments are perhaps a rallying call, rather than a warning. Either way, McCluskey’s intervention dripped with dissatisfaction.

Whatever occurs in the coming months and years, potential candidates in a Labour leadership contest are likely to require the nominations of at least 15 per cent of MPs and MEPs. Suggestions from Unite and Momentum that this threshold be reduced to 5 per cent have been opposed by Unison and the GMB. Without this change, it would be difficult for a member of the PLP’s Socialist Campaign Group to succeed Corbyn.

The unions provide a third of Labour’s funding. It is the party that faces a threat to its existence, not the labour movement, argues a smart operator at the heart of the movement who has ambitions to become a Labour MP. “In the unions, we’re just getting on with arguing for pay rises, saving jobs and protecting public services. The blunt truth is, much of the time, the Labour Party doesn’t feel particularly relevant to what we’re doing,” he says. “Jeremy will always come along to a rally . . . But nobody expects [him] to win the next election. Can anyone in Labour really win it? Everybody was saying in 2015 that Labour was going to lose again, before Jeremy’s full-blooded socialism, so it’s not really his fault, is it?”

This judgement goes a long way to explain why exasperated union leaders aren’t hammering at the leader’s door with one hand while gripping his P45 in the other.

Frances O’Grady, the general secretary of the Trades Union Congress, is known to be frustrated, yet she bites her lip and refrains from commenting publicly on Labour’s predicament. Most of the 51 unions affiliated to the TUC, including those in education and the civil service, aren’t constitutionally linked to Labour.

For Matt Wrack, Corbyn is still worth fighting for, to move the party in a different direction. “The election of Jeremy Corbyn has marked a sea change in Labour’s attitude to the trade unions,” he says. “One very clear example of this is in relation to public-sector pay. In 2015, and before Corbyn, Labour’s then shadow chancellor [Ed Balls] wrote of the need to back the Tory freeze on public-sector pay. It was a slap in the face for public-sector unions, especially those affiliated to the Labour Party. Since Corbyn’s election, that approach has gone from the front bench – it’s as simple as that. The new leadership has demonstrated a very clear commitment to working with the unions . . . That is a breath of fresh air compared with the union-bashing we got from Blair.”

But what about Conservative union-bashing? EU-endorsed workplace rights – paid holidays, equality, consultation – will not be guaranteed automatically in post-Brexit Britain, freeing the Tories to attack employment practices.

Trade unions will be confronted with a painful choice, should Corbyn fight and lose the 2020 election. Socialist policies are inspiring, but without power they never get further than the pages of the manifesto. The movement’s solidarity is with working people, rather than just one man. Corbyn would be unwise to bank on sustained union endorsement. In Labour politics, there is no such thing as a blank cheque.

Kevin Maguire is the associate editor (politics) of the Daily Mirror