The paint was peeling, and chunks of ceiling seemed precariously balanced, as we sat in a derelict swimming pool in Govanhill community centre, in Glasgow. Inevitably, the surroundings provided many of the passionate speakers at the first Festival of Ideas with a handy metaphor for the union as they elaborated their project of “live as if in the early days of a better nation”. From where I was sitting, in the deep end, I saw there is a real danger that over the next 10 days we will profoundly miss the point.

Listening hard, it felt like entering an Alice in Wonderland world because many of the words we think we understand turn out to have radically different meanings in this exhilarating debate north of the border. Most importantly, for many people independence is not about nationalism at all, and certainly not ethnic nationalism (a mistake still being attributed to the yes voters).

But it’s not even about the revamped civic nationalism of the Scottish National party either. Many people are quite clear, they are voting yes because they want a new form of politics, better democracy and social justice. It’s a massive protest vote against the status quo.

There are varying degrees of idealism, self delusion and realism about the chances of Edinburgh delivering on this promised land, but the point is that increasing numbers think it’s worth a try. You can hear the echoes of Thomas Carlyle in the stirring rhetoric on the evils of materialism and neoliberalism. The dubious track record of Alex Salmond on this front is dismissed as irrelevant; post independence, new political parties will form in this brave new world.

There are two implications of this. Regardless of the referendum outcome, the campaign has proved a catastrophic failure for Labour. It is no longer an effective vehicle for democracy and social justice in one of its oldest heartlands. Its vote has collapsed. The word most commonly used in conjunction with Labour is ‘corrupt’.

A shrill hysteria has now crept into London-based government and media responses. Words such as foreign and amputation are being thrown about alongside talk of passports and borders. Britain is once again hailed as broken (I blame alliteration). But as the rubble of nationalism is cleared away, there is a second implication as another word is being reinvented: Britishness.

Repeatedly, Scottish yes voters insisted they would remain British. The Irish writer Fintan O’Toole agreed: Ireland was still British. The point made was that when Norway split from Sweden in 1905, Scandinavia emerged as a powerful common identity.

This definition of Britishness is about a shared history and language, and the common reference points of culture and ideas that provides. We are all part of the British Isles, and nothing is going to change that rich interdependency as we continue to fall in love, make babies, make friends, exchange ideas, trade, and visit each other.

As an Atlantic archipelago of islands on the edge of Europe, we have far more in common with each other than not, and do not necessarily need a political union to make that a reality. What we will need is new institutions of collaboration across the nations and regions of the isles.

It’s a dramatic redrafting of the story of Britain. In recent decades, it has been self-evident that the Britain of empire and monarchy, of army and church, is history. Britishness has historically been seen as an export, more about how to project ourselves on to the world than how we want to live together. Attempts to revitalise Britishness by claiming human values, such as fair play, rang hollow. The Better Together campaign has been dogged with the absence of any emotionally resonant vision of Britain to articulate as a defence of union.

This idea of Britain is already lost regardless of 18 September’s verdict. That much is commonplace. The point, then, is what you do about it. England will have to find its way to a new relationship, one among equals with the other nations that share these British islands.

Agreed, England’s impulse for much of the last millennium has been to dominate the cultures and nations of this archipelago, but there are plenty of long overdue reasons why its famed pragmatism could see the sense of recasting those relationships now, given our shared economic interests and environmental resources.

Not all relationships within the British Isles would be configured at Westminster, although England will, by virtue of its size, be a valued partner. Ireland is likely to play a midwife role in the event of an independent Scotland. Northern Ireland’s history and connections are more with Scotland than England, and O’Toole rightly suggested that Northern Ireland should be a priority for any independent Scotland.

Why choose the metaphor of divorce, with all its associations of bitterness, recrimination and pain? At a point of history such as this, metaphors are vitally important because they have a way of becoming self fulfilling.

Benedict Anderson famously said nations are “imagined communities”. Scotland is busily imagining itself; England is slowly stirring to the same task, and with plentiful resources of radicalism and diversity from which to draw. What we now have to do is use our shared geography. For decades, we have been transfixed by the white cliffs of Dover as a symbol of nation. But if we look west and north to those who share these islands, we can serve our common history and recognise all the unions – of families, cultures, friendships, environment and economy – that will continue as powerfully as ever after 18 September, whatever the vote.

• Madeleine Bunting is researching a book on Scotland and England, to be published by Granta in 2015