The Brexit vote has not only exposed deep socioeconomic fractures in British society – it has also invented new ones. Identity politics has taken hold as never before.

Recently an Etonian called me (the daughter of a car mechanic) the elite. Apparently my ethnicity and London upbringing make me the enemy of the population that matters most right now: the white working class. This accusation was a reminder of how false and divisive these new labels are.

I grew up in east London, before it became the cool playground of hipsters it is now. It was a neighbourhood full of white working-class people (including David Beckham); and, while it wasn’t perfect, the process of growing up together, hating the same teachers, dating each other (not David Beckham) and sharing in good times and bad meant that solidarity crossed race lines. Fast-forward 20 years, and I’m now told by Etonians the white working class see me as the enemy. Is this true?

On Tuesday, the Runnymede Trust and CLASS launched a series of essays seeking to examine the legitimacy and implications of this narrative. We conclude that the “white working class” label is not benefiting the white working class, or society more widely, and that many of the assumptions that underlie this narrative are just plain wrong.

Let’s start with the accusation that the white working class are racist. In my essay, co-written with Ellie Mae O’Hagan, I recall the racism I faced at University of Oxford where my fellow students asked me questions such as: ‘Why do black people cause crime?’ The idea that racism is confined to the white working class is ridiculous, and akin to the idea that it is only the poor that commit crimes. After all, it is the white middle class that is in control of the public spending cuts that are disproportionately hitting minority ethnic women, and discriminating against people with African or Muslim names in the job market. Racists and racism exists across society.

Recent analysis from Policy Exchange highlights how using this false depiction of the white working class can lead us into dangerous territory. The authors of this study, David Goodhart and Eric Kaufmann, draw on a small survey of UK and US citizens to tell us that “racial self-interest” is not the same as “racism”, concluding that it is fair for white Britons to defend white identity.

This is flawed logic. We wouldn’t use a “religion’s self-interest” argument to justify Islamic State. Wasn’t “white self-interest” used to legitimise the slave trade? As well as being wrong, these ideas also justify the concerns about immigration on racial grounds, and suggest that our racial identity is our main group attachment. Brexit may leave the UK without a trade deal, but an equally important worry is that it turns back progress on community cohesion.

The second, related myth to dispel is that the working class is all white. A large proportion of the working class – often defined as those in manual or elementary jobs or on low incomes – are from minority ethnic populations.

My mother-in-law, a lunchtime play worker (or a dinner lady if you went to school before 2010), was made redundant alongside all of her colleagues this week. These dinner ladies – who represent the whole spectrum of race – are all in the same boat. Public spending cuts mean they are all losing their jobs, and as a group of women without higher qualifications they are all faced with dead-end, low-paid and insecure work. Why does it help to divide this group when they have so much in common?

This really gets to the root of why the white working class narrative is so problematic. It divides a group that when united and mobilised can be a real force for change.

Take the Living Wage campaign. It was started in 2001 by a group of low-income parents who were struggling to live on minimum-wage jobs, and quickly grew to include churches, mosques and a vast array of local community groups. To date the campaign has lifted an estimated 70,000 families out of working poverty. The white working class and the minority-ethnic working class aren’t enemies – they are companions in a fight against economic inequality.

It’s not hard, then, to see whose agenda dividing the working class is serving – that of unscrupulous bosses, CEOs now earning 386 times the national living wage and the policy-makers who are creating the conditions that allow this to happen. Not for the first in history, working-class people are being used as pawns to maintain privileges at the top.

This endless exercise of putting ourselves in boxes is not helping us to foster a broader and inclusive British identity, nor tackling the real problems that the whole working class face: finding good jobs, decent housing and having access to properly funded public services.

This week saw the International Day for the Elimination of Racial Discrimination. We’d do well to remember how important language is in sowing seeds of distrust and hate. The “white working class” narrative is leading us down a road of nostalgia for a white Britain. We need to stop it in its tracks.