Anyone expecting the revolution will surely have walked into Liverpool’s gleaming Convention Centre and wondered where it was. The Labour party conference might now be Jeremy Corbyn’s domain, but it was all surprisingly familiar: a great wall of men in dark suits, fringe meetings with titles like “What’s ahead for consumers in a digital future?” – and, by way of a cruel pantomime, the disoriented sons and daughters of the Blair-Brown years, still wondering how to respond to what has happened – and, on the evidence I glimpsed, not getting much further than mouthing such tired tropes as the need for “an over-arching narrative”.

In glaring contrast, the most fulfilling and enjoyable event in Liverpool was The World Transformed, the five-day “festival of politics, art and culture” put on across town by Momentum. Here, most of the sessions – spread around a church-turned-arts centre, which felt as homemade and human as the official conference was cold and alienating – were designed to allow as much participation as possible, and thereby spark the maximal level of debate. You could tell something exciting was afoot by the hubbub that extended from the tiny reception area out into the street, and beyond.

I spent a day there, contributing to an invigoratingly non-doctrinaire conversation about the politics of Englishness – and then watching a two-hour session that spoke volumes about one of left politics’ emerging fault lines. This debate was titled “Building a progressive majority”. On one side sat two people close to the Corbyn project: the veteran Labour leftie and Momentum founder Jon Lansman, and Rhea Wolfson, a Scottish Momentum activist recently elected to Labour’s national executive. On the other were the chair of the left pressure group Compass, Neal Lawson, and the Green party’s co-leader, Caroline Lucas. Around 200 people participated: as the conversation went on, it became both more impassioned, and increasingly fascinating.

‘If you want a sense of a remodelled Labour party, think of Jonathan Reynolds happily in alliance with Clive Lewis [pictured].’ Photograph: Jon Super/EPA

Lansman is a fantastically capable organiser, with an instinctive understanding of many of the tensions and complications of Corbyn and his allies’ position, and an honest sense of Momentum as “a work in progress”. But he is also someone apparently too reluctant to move away from the verities of the last century. The Green party, he suggested, might be a laudably progressive setup, but it might be best off simply merging into Labour, like the Co-operative party did back in 1927. Proportional representation, he reckoned, was much less of an issue now the Labour party was on the road to internal democracy – and, in any case, remained a dangerous idea, which supposedly gifted small parties with too much influence and would adversely affect the left’s chances of acquiring power.

Wolfson parried points about Scotland with formulaic jibes against the SNP (“Nationalists!” shout far too many Labour people, as if that will settle the matter), full of the idea that sooner or later the straying Scottish millions would come back to their natural political home. It made for an odd spectacle: people from the supposed radical left, with instincts that were often disappointingly conservative.

A lot of the audience had a rather different take. Some said their affinity with Labour was complemented by occasions when they had voted for other parties. They liked Caroline Lucas, a lot. They also liked the idea of, as one speaker put it, “negotiating the future” via a revolutionised voting system, rather than imposing it with the support of a small minority of the electorate.

These were not the hardliners and ideological desperadoes that some people might imagine: their politics felt open, self-critical and realistic about the huge tasks it faces. They may not yet have a clear idea of how a new left politics might decisively cohere – but no one (not even gobby newspaper columnists) does, as yet. The point is to at least begin with a sense of how it might start to mesh, and the breadth of people who will have to be involved.

There are deep and overlooked differences between these people and some of the Labour voices currently shouting the loudest. And, as events in Liverpool ground on, an obvious truth began to rise to the surface. On both the left and right of the party, the two strands most embroiled in the party’s current faction-fighting (and, to be blunt, enjoying every minute) will have the least to do with what eventually emerges from the mess.

What we might think of as the hard right and hard left might think of themselves as being light years apart, and locked into an epochal battle for control. But they are both creatures of the 20th century, equally convinced that Labour alone has the answers, that arcane debates about party committees and conference resolutions represent a worthwhile use of human effort, and that absolutely everything always centres on the question of whether Corbyn and his allies should stay, or go.

One side wants expulsions; the other deselections. On the left, some people seem nostalgic for the 1970s; on the right, eyes mist over at the mention of the 1990s. Neither tendency, it seems to me, will have much to do with the English left’s long-term future.

The two strands embroiled in the fighting will have the least to do with what emerges from the mess

Meanwhile, a tantalising sense of something different is starting to emerge, not just among what one Momentum activist tentatively described as “a new, modernised left”, but also in some more surprising places. Over the next few months, pay attention to Jonathan Reynolds, the Greater Manchester MP – tipped for a return to Corbyn’s shadow cabinet – and representative of Labour’s supposed “centre”, who enthusiastically makes the case not just for changing the voting system and calling time on Labour’s monopolisation of left politics, but a universal basic income (interests he shares, incidentally, with the shadow chancellor, John McDonnell).

To get a sense of a remodelled Labour party that might eventually emerge from all this turbulence, think of Reynolds happily in alliance with, say, Clive Lewis, the Corbyn loyalist whose travails on Trident pointed to a politics grounded not just in a quest for a radically different Labour politics, but also a smart sense of priorities. But picture also an open, porous, thriving movement, substantially rooted in a new Labour party, but also present far beyond it.

This is not about 2020, or an election that Corbyn says – for internal tactical reasons, presumably – might happen earlier than that. Politicians have to talk about single electoral cycles; journalists and commentators too often seem unable to conceive of things in any other terms. But anyone with any grasp of Labour’s predicament well knows that reinventing its politics will be a much more onerous business, spread over a longer time frame. The hoary old Gramsci quote about pessimism of the intellect and optimism of the will just about fits the essential story. This remains a deep crisis, too often worsened by the politics of the past, on both left and right. But there are also tantalising glimpses of the future, and plenty of reasons to keep faith.