In the end, it was the selfies that gave it away. Jeremy Corbyn guards his privacy so fiercely that even his closest allies didn’t know exactly where in the West Country he would be on holiday during the Easter recess. So they were as surprised as anyone when, in the last week of March, photographs of their beaming boss posing with fans in the seaside town of Exmouth began to appear on social media.

That reticence to submit to the management of his aides is one of many ways in which Corbyn differs from most party leaders. It partly explains why, even in a reliably Conservative redoubt such as Exmouth, he is constantly surrounded by passers-by who are keen to get a photograph and have a chat. Unlike some of the bands he will share a stage with at Glastonbury – the Labour leader will be addressing the festival in the weekend after the EU referendum – there is nothing manufactured about Corbyn.

His decision to cut short his holiday to visit the steelworks in Port Talbot, which are under threat following Tata Steel’s decision to sell off its British operations, was entirely in keeping with the Labour leader’s style of politics. It came from the heart and left his office scrambling to keep up – and it also left David Cameron, who opted to remain in Lanzarote, looking callous.

The forces that threaten to destroy Port Talbot’s steelworks could have been scripted in the Labour leader’s office, so perfectly do they illustrate the core preoccupations of the Corbyn project. A linchpin of the local economy – and a strategic national asset – is owned not by Britain but by an Indian conglomerate, which is powerless to maintain the value of its business against heavily subsidised steel production by the Chinese government. (An autocratic state that, lest we forget, George Osborne wants to let control other key infrastructure, such as nuclear power stations.)

Imagine for a moment that the crisis had occurred not in 2016 but in 2013, while Ed Miliband was leading Labour. His aides would have talked about “winning the big arguments”, doubtless excitedly passing among themselves an article by whichever right-wing columnist was prepared to concede that the free-market model had a few small flaws. Miliband would have posed for photographs outside the steelworks, making Cameron – who would have opted to remain in Lanzarote – look callous.

But then, inevitably, it would have fallen apart. Miliband would have attempted a balancing act: offering on the one hand a strident criticism of global capitalism and all its works and, on the other, attempting to reassure big business that free enterprise would be safe under Labour. The result, as so often under Miliband, would have been to leave no one with a clear idea of what, exactly, the party would do differently.

Corbyn, by contrast, is not frightened to use what one ally jokingly described as “the N-word”: nationalisation. Under Corbyn, the answer to the question “What would Labour do?” is never: “I’ll get back to you.” If Vladimir Lenin’s communism was “Soviet power plus electrification”, Corbyn’s policy programme is Milibandism minus dithering. As a Corbyn insider puts it: “We are more confident in ourselves.”

Overconfidence brings its own pitfalls, however. The great illusion that all opposition leaders have to maintain is that they have any power at all. As an aide to Miliband once observed: “The polls all say we’re weak. Of course we are. We’re not in power and we can’t do anything.”

Corbyn’s call for parliament to be recalled merely illustrated the impotence of the leader of the opposition. He has form in this area: following Iain Duncan Smith’s resignation from the government over cuts to disability benefits, the Labour Party called on George Osborne to follow suit. Nothing happened. This approach risks turning moments of opportunity into displays of weakness. That further worries the Parliamentary Labour Party, most of whose members fear that Corbynism will deliver the same electoral result as Milibandism, minus 50 seats in the House of Commons.

That said, the scale of parliamentary discontent towards the party leadership is smaller than it seems when amplified through the media, which are largely hostile to the Corbyn project or starved of Corbyn-friendly sources. Most Labour MPs believe that either their leader or John McDonnell, his likely chosen successor, will be securely in place until the 2020 election. The disaffected should, in the words of one, “pipe down, use this time to hold on to as many marginals as we can and to think about the policies we should stand for after”. Others – with Chris Leslie, the former shadow chancellor, acting as their unofficial chief whip – believe that a coup can succeed. Yet even the group that believes that Corbyn is replaceable cannot agree on who should replace him.

As a result of the division and uncertainty, Corbyn and his allies will remain in their positions for the foreseeable future, even if the local election results in May are as bad as Colin Rallings and Michael Thrasher predict. These respected academics project that Labour will lose 150 council seats on 5 May, unprecedented for an opposition this early in the parliament. Yet the great prize of London looks likely to fall to Labour’s Sadiq Khan. In reality, the results in May will be the political equivalent of the Mirror of Erised in Harry Potter: people will see in them whatever they desire.

Because of all this, Jeremy Corbyn is safe, if he wants to be, until the next general election. The challenge for him is to whip his back-room operation into shape, preserving his considerable grass-roots appeal while ensuring more than a few day-trippers in Exmouth get to know him. Professionalism and authenticity? Well, the headliners at Glastonbury seem to manage it.