I will never forget the day I joined an English Defence League march in Chelmsford, Essex, in the run-up to the Brexit vote. I went as a journalist, and I wasn’t expecting it to be a comfortable experience. But the most shocking moment was not what I predicted. Instead of threatening me with directly racist slurs, a senior figure at the march told me he wasn’t fussed by my presence. “You’re OK,” he said. “You speak English properly. You know our ways. You’re like us. It’s the others we have a problem with.”

By “others”, he meant Muslims – the EDL’s most frequent target – or any other visible minorities he deemed to have made insufficient effort to assimilate into British culture. It struck me as the most chilling and insidious form of racism of all: he was, in effect, saying, “People who come to England are acceptable to the extent they attempt to mimic us.” Underpinning that is a confidence in one culture’s inherent superiority over others. It’s for exactly this reason that it is becoming more widely recognised that assimilationist thinking – the idea that a particular culture is preferable, and that others should therefore adopt it – is a racist ideology.

“Integration is not assimilation,” said the UK’s most senior counterterrorism officer, Neil Basu, this week. Basu was pointing out that the latest research on terrorism shows that people with extremist views are moved to violence not because they aren’t “assimilated” but because they feel excluded. “Create a sense of belonging, while not forcing people to give up things they may hold as sacred,” Basu rightly recommended. “If we fail … we risk social exclusion turning to violence.” But too many people who profess their support for integration are really talking about assimilation.

The pressure to downplay your culture, your identity or your pride in your heritage to gain the approval of the majority around you risks further excluding people. Yet it is a pressure many of us recognise. Earlier this week I hosted a public conversation with the London mayor, Sadiq Khan, where we talked of our common experience in embracing mispronunciations of our names to make lives easier. His “Sad-eeq” is really meant to be pronounced “Saad-iq”. My “Afua” is really meant to be pronounced “Ef-wa”. We have both embraced a version others in this society find less onerous to grasp.

Khan himself is clear on the difference between assimilation and integration. He sees integration as about encouraging meaningful interactions not just between people of different ethnicities, but also different ages, social classes, sexual orientations and abilities.

‘Sadiq Khan sees integration as about encouraging meaningful interactions not just between people of different ethnicities, but also different ages, social classes, sexual orientations, and disabilities.’ Photograph: Catherine Ivill/Getty Images

This is something all governments should take more seriously. But the question is, how much can be done against a backdrop of cuts to the kinds of cultural activities and community services that have naturally facilitated integration for decades?

Research has shown that income inequality, not the extent of ethnic or religious diversity, is the most significant factor associated with lower levels of trust within a society. While the government claims to be pro-integration, its policies make this far harder. The housing affordability crisis disrupts people’s sense of community and fuels alienation. And, far from encouraging migrants to try to become citizens, the Home Office has raised the cost of citizenship by more than 25% in recent years. An adult citizenship application now costs £1,330, a good chunk of which is profit for the government. Our prime minister has still not been held to account for his own divisive, bigoted language towards minorities – just one example being his comments comparing women who wear burqas to letterboxes.

The 2016 London mayoral campaign was a case study in how deliberately promoting segregation and division can still be a mainstream political tactic. Khan’s Conservative challenger, Zac Goldsmith, ran a campaign that even other Tories acknowledge was divisive and racist in its attempts to spread distrust of Khan because of his Pakistani heritage. It was the idea of his strategist, Lynton Crosby. Yet at the very moment Khan was being inaugurated as mayor, Crosby was being knighted in David Cameron’s honours list.

It may be naive to hope for a more sophisticated discourse on integration when we have a prime minister who is comfortable with using racist and degrading language. But the root causes that motivated some people to vote for Brexit – feelings of social exclusion, of not being at home in one’s community, of rising levels of inequality and of feeling left behind – are reminders that creating a cohesive society is not an optional luxury. And if we fall into the trap of old-fashioned assimilationist thinking, we will continue to create more problems than we solve.

• Afua Hirsch is a Guardian columnist