What makes a person working-class? Being northern? Working in a factory? Being a plumber? Being white? Voting Brexit? If you watch TV or read a newspaper you will probably think all of the above. Unless you’re actually working-class, that is. From David Dimbleby declaring on the night of the EU referendum result that working-class votes were the decisive factor in the Brexit referendum (wrong) to TV dramas depicting the lazy and criminal, the mythology built about working-class people is wide-ranging and often damaging. This is important, because if we see class as purely about culture, we ignore the role of the economy, the state or community.

New research on low-income Londoners from the Centre for Labour and Social Studies and the Runnymede Trust found that while just over half identified as working class, almost all shared what could be described as a working-class experience. On the negative side, this included feelings of being “dehumanised” by impersonal public services and excluded by gentrification. Social mobility didn’t work for many in a system rigged for privilege. However, there are signs of community-led solidarity.

Today, working-class people include black people, white people, old, young, people in social housing, people in private rented accommodation, migrants and many others. What unifies them is the way in which capitalism and its supporting state infrastructure chews them up and spits them out. They live precarious lives, face prejudice, have very little power and voice in their day-to-day interactions with work or the state, yet take pride in the place where they live.

So why isn’t this diversity reflected in our perception of the working class? One reason is the classic political tactic – divide and rule. Nigel Farage would have vanished years ago if people had rejected a division between the black and the white working class.

In our interviews, we found this division has worked so well that people of colour who were working class didn’t see themselves as such because “we don’t go to the pub”. Some may ask: why does this even matter? Peoplehave the right to identify however they want. But imagine the power of uniting the working class across the country – we would counter the huge power and wealth that sits at the top of society. It’s no coincidence that inequality grew rapidly when trade union membership declined – neoliberalism took apart the apparatus that brought workers together and gave them power. More than that, working-class solidarity was the basis of huge strides in British history, including the establishment of a modern caring state. With a shared class identity, we would rewire social justice.

This is also about the story we tell ourselves about who we are. Imagine the language of “traditional working class” was binned, and instead we came to understand the working class as a diverse group of people at risk of being exploited by the elite; even that Britain has long had a multi-ethnic working class, including my great-great-grandparents who worked as indentured labour in sugar cane fields in Fiji, with the profits ultimately flowing back to the UK government’s coffers. They were the British working class.

No one has waged class war more than the Tories, whether it be culling trade unions, selling the idea that we have more freedom when the state isn’t around to support us, and even that inequality is good for us. Yet we found examples of working-class communities coming together to fight for local justice. Even as estates and factories are demolished, and communities split up, still the bonds of unity in adversity remain. The working class is down but not out.

• Faiza Shaheen is director of the Centre for Labour and Social Studies and Labour PPC for Chingford & Woodford Green