I got to know Green Street, the British Asian equivalent of Oxford Street, when my sister got married last year. Newham, home to Green Street, is Britain’s most diverse borough. That diversity brings upsides: when it came to bridal saris and jewellery, my sister had no less choice than if she’d been shopping in Delhi or Mumbai. But it also brings challenges: how do you ensure people from very different cultures and backgrounds live peacefully side by side?

Is this best done by forcing people beyond their comfort zone, encouraging them to mix? Or by ensuring that minority communities have their own organisations to represent them and provide services that cater for their particular needs, with less of a focus on whether and how mixing happens?

If the debate in thinktank seminar rooms is anything to go by, this argument was settled a decade ago. The “multicultural model” fell out of favour in the early 2000s following riots in Bradford, Oldham and Burnley. Experts condemned it for permitting communities to live “parallel lives”, thought to be a factor in the unrest.

What surprises me about this debate is how it tends to be conducted in the currency of national, rather than local, politics. Yet the levers for managing diversity, to the extent that they exist, are overwhelmingly local. So in an Analysis programme for Radio 4, I applied a more local lens. We went to two very diverse places – Newham, in East London, and Leicester, in the East Midlands – where the councils have taken a very different approach.

What was striking about Leicester was that the multicultural model so discredited at national level was, until recently, still in evidence. The council has funded a number of groups representing ethnic and faith minorities to act as a point of contact with the council. It has also made significant resources available to minority groups. Is this so problematic? After all, Leicester has not seen the sort of unrest that characterised places such as Bradford in the early 2000s. But a range of Leicester residents we spoke to painted a picture of a city that has become more segregated over time. Many were concerned about the divisive impact of Leicester’s multicultural approach. Even a representative of a minority organisation that has benefited from funding thought the model of speaking to people via community leaders has long had its day.

So why has a discredited approach persisted in such a city? I’ve come to realise you can’t understand diversity policy without understanding local Labour politics: it is usually in Labour-controlled areas where you also see high levels of diversity.

The multicultural approach developed out of a faction of the Labour party in the 1970s, keen to tackle racism and help immigrants settle in. But over time it became intertwined with Labour’s voting base: local politicians developed close relationships with community leaders, who helped deliver votes from their neighbourhoods. This phenomenon is most evident in places such as Tower Hamlets and Bradford West, where Labour suffered mini earthquakes when the minority vote temporarily switched sides. But people we spoke to believed it has also been a factor in preserving Leicester’s multicultural feel and helped cement it as a firmly Labour city.

In Newham, Labour mayor, Robin Wales, influenced by what went on in neighbouring Tower Hamlets, is critical of the community leader model and has taken a contrasting approach: the council will only fund groups running services and events that bring people from different minorities together. He’s cut funding for translation services and is spending more on English lessons.

It’s not yet clear how deep an impact this is having. But encouraging mixing and learning English seems to me a better use of scarce resources than funding groups to represent specific communities. Newham is often held up as a model in the national debate, but I wonder how many Labour councils are emulating the mayor’s approach?

I can’t see second- and third-generation minority Britons continuing to vote along community lines in the same way as their parents may have done. This might put Labour’s ethnic minority vote, long taken for granted, at risk. But it may also mean local Labour politicians have more freedom to explore the Newham approach.

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