The Manchester I left behind in 1997 seemed to me a place of racial harmony. Asian and white children had mixed happily in my small Church of England primary school in the city's southern suburbs. The same was true of my large private secondary school, where the number of Muslims was just about matched by the Jewish students. Racial or religious tension was unheard of in either. And Mancunians of all creeds and colours mingled without bother in the city-centre pubs and nightclubs that I knew. But just four years later my home city was in the headlines in a way I never expected. In May 2001, the town of Oldham, which lies on the opposite side of Manchester to where I grew up, experienced some of the worst urban violence seen in Britain for decades.

It was described as a race riot. Tensions that had apparently been building for weeks between the white and Asian communities boiled over on 26 May. The television news bulletins showed lines of armoured police battling ranks of Asian youths. A pub was fire-bombed. So was the home of Oldham's deputy mayor, Riaz Ahmed. I remember thinking: was this a part of the same harmonious city in which I had grown up? Had I been wrong about the true nature of race relations in Greater Manchester? And Oldham was only the first conflagration that summer. In the following months, the flames reached Bradford and Burnley, two other northern English towns with sizeable Muslim populations. The images were the same in all three: angry Asian youths clashing with white men and battling it out with the police.

Those riots shocked me profoundly. But they also shocked Britain. The Labour government commissioned a report into the violence by a local-government official called Ted Cantle. And he came to a conclusion that, although the racist far right had played a role in stirring up tension, the underlying cause of the riots was Asian and white residents living "parallel lives". Such was the geographical segregation between the two communities, found Cantle, that these places were like a sea of petrol, just waiting for a spark to set them alight. That finding was difficult enough to absorb for those such as myself who had assumed that Britain was fundamentally well-integrated, where people of different backgrounds, by and large, rubbed along fine. But what another local-government bigwig, Lord Ouseley, had to say about the violence was even more uncomfortable. He wrote a report arguing that what we had seen was "self-segregation": Asians had chosen to live apart from the white community.

The British right leapt on these findings like hungry wolves. They declared Ray Honeyford, the Bradford headteacher who criticised Asian cultural practices in 1984, vindicated. And the political discourse on race and religion suddenly took on a more intolerant tone. Racial and cultural diversity were no longer seen as adding to the quality of British life; they were now a "problem". And British Muslims were the biggest problem of all. Support for the BNP rose in segregated northern English towns. The lowest moment came when it transpired that three of the suicide bombings in London on 7 July, 2005 were perpetrated by British Asians from Leeds. A few months after those attacks, the then head of the Commission for Racial Equality, Trevor Phillips, gave a speech in which he depicted Britain "sleepwalking to segregation". The multicultural dream was declared over.

But something interesting has happened since that rude awakening. Academics have begun to question the findings of those initial reports on the riots. Cantle's "parallel lives" thesis was challenged by Ludi Simpson and Nissa Finney from Manchester University, who pointed out that places such as Bradford, Burnley and Oldham were much more ethnically mixed than this soundbite implied. And Lord Ouseley's "self-segregation" finding was contradicted by research by Yunas Samad in Bradford last year. Samad found that geographical segregation was a consequence of "white flight" rather than separatist Asian attitudes. There have been other challenges to the idea that Asians do not integrate. A 2009 Gallup poll found that the Muslim community is much more likely to identify strongly with Britain than the rest of the population. It also showed that they are collectively more in favour than white Britons of mixed ethnic communities.

These are very different pictures. So which is closer to the truth? Are British Muslims self-segregators, culturally antithetical to British values, a community that incubates the virus of religious extremism? Or are they patriots and victims of white racism, a misunderstood and slandered migrant community, like so many others before them, from the Jews to the Irish? It is exactly a decade since the Oldham riots, the violence that prompted this revolution in race relations. Last week, I travelled there – and also to Bradford and Burnley – in search of an answer.

Parallel lives?

The most striking feature of all three of these former outposts of the mill industry is the natural beauty of their surroundings. Each is nestled amid rolling green moors. The ethnic segregation, however, is a fact. I drove with Ansar Ali, the head of the Manningham Housing Association, which helps Bradfordians to find affordable homes, for a good 20 minutes before we left the city's Asian district. I also walked in large areas of Burnley and Oldham that predominantly were host to Asian families. There is a caveat here. The idea that one can pass through places such as Glodwick in Oldham and Stoneyholme in Burnley without seeing a white face is nonsense. I saw several white residents in the Muslims areas of all three towns. Yet segregation – in the sense that certain areas are considered predominantly "white" and some predominantly "Asian" – is a reality. And segregated housing has led to largely segregated schools.

To some, this in itself does not matter. Councillor Howard Sykes, the plain-speaking outgoing head of Oldham Council told me: "I don't necessarily see segregated communities as a problem. Can you blame somebody who chooses to be near their relatives, near the facilities they want, near the shops that sell the things that they want, and where their place of worship is? No. The point is, where them people do mix – workplace, sport, culture, education, whatever – they do share some common values."

Others disputed the idea that geographic segregation means that people must live "parallel lives". Nineteen-year-old Adib Asif lives in the Glodwick district in Oldham, just off Waterloo Street where the police battled rioters in 2001. From his mother's spotless living room, he told me matter of factly of his white friends and how they drive from their own areas to pick him up when they go out to socialise. Adib is a student of Oldham College, a further-education training centre that has been judged outstanding by Ofsted.

The softly spoken head of that institution, Alun Francis, is keen to add some nuance to the picture of segregation. "It isn't true to say that communities in Oldham don't mix because nearly all of them come to this college or the local sixth-form college," he said. "From 16 to 18, nearly all people in Oldham grow up mixing with people from different social backgrounds."

Economic pain

Housing segregation is one fact of life in these towns. But economic pain is another. Bradford and Burnley are home to some of the poorest wards in England. All three places have high levels of youth unemployment. And some regard this, rather than segregation, as the real root of social tensions. Mushtaq Khan, the director of the Aksa Housing Association in Oldham, told me that the issue of segregation is really a red herring and that the only way to alleviate Oldham's tensions is to build more good-quality, affordable homes and to create economic opportunities for both communities. Alun Francis agrees.

"The people in Glodwick have the same aspirations for their children to become doctors and professionals as everybody else does," he said. "If their children are successful in that, are they going to stay living in Glodwick?" Get the economics right, according to Francis, and the segregation should naturally erode.

But Howard Sykes of Oldham Council is unconvinced by the argument that the town's problems can be put down to lack of opportunity. "Have we not just had 10 years of a booming economy?" he asks. "So if you follow the logic, we would have had all those people in work. And they would have only recently become unemployed. That hasn't happened has it? If everybody who is currently unemployed had a job, would all this go away? Don't think so."

Sykes, and others I spoke to, argue the key is raising aspiration in both Asian and white areas. I heard this elsewhere. One evening last week, I sat down to dinner with an old school friend, a Muslim from east Manchester. I related to him what I'd been told about how the inhabitants of these three depressed towns often lack the money to renovate their terraced houses. "Never mind their houses" said my friend. "Some of these people can't renovate themselves."

Northern pride

The people of Bradford, Burnley and Oldham might disagree on the root causes of some of their communities' difficulties. But they seem to be united about one thing: anger at the national media's promotion of a grossly distorted vision of their communities. Time and again I heard the complaint that the media come in and stir things up in order to tell a simplistic story of segregation and inter-racial animosity.

"It's so easy," says Howard Sykes. "Someone from London jumps on a train and comes. It's very easy to get a story in this town to get the answers that allows you to write the story you've decided the story is." When I visited Alun Francis at Oldham College, he had just ejected a BBC Newsnight presenter and film crew for, as he saw it, exaggerating ethnic tensions between Asian and white students in a report. But it was not just officials and teachers who were frustrated. Over and over, ordinary people told me how unfair it is that a minority of racists or criminals in either community should be allowed to define the reputation of the majority.

The people of Bradford also seemed to me to be united in pride. Why, they asked, did the media never cover the Bradford Mela festival, held in June, at which all races come together in celebration? There was pride in Oldham too. Rabina Kauser, who works for the Aksa Housing Association, told me: "I'm proud to be from Oldham – proud of the history, the people. The riots made it look like it's bad, but it isn't."

Misleading diagnosis

So where does that leave us? What is the answer to the original question about the nature of British Muslim communities in these towns? I have been left with the impression that the revisionists are right: the original post-riot reports on the northern English mill towns told a misleadingly simplistic story. The parallel-lives thesis was exaggerated. I saw with my own eyes that contact and friendship between whites and Asians can and does exist even when they do not live side by side. Asian self-segregation seems to me another misleading theory. Most of the Asians I spoke to were perfectly happy with the idea of more mixed neighbourhoods. Segregation seems to be more a consequence of an inadequate housing stock than a collective desire to live apart. The residents I spoke to were proud to be British and proud to be Muslim. And they were frustrated by the suggestion, put forward so often by politicians, that their community is a hotbed of forced marriage and religious extremism.

The post-riots reports also underplayed the importance of "white flight" as a cause of ethnic segregation. My eyes were opened to this truth in Burnley. Skirting around the town centre, I came across a white, 48-year-old window cleaner and asked him directions to the Asian district of Stoneyholme. He showed me the way, while telling me that he used to live in that district but that his family had moved out he was 10. Why? "They didn't like what was happening. The Asians move in and take over an area. They felt like aliens in their own country." I asked him what would happen if he, a white person, went to Stoneyholme today. "I'd probably get abuse". So off I strolled into this lion's den of prejudice. And what did I find but Andrew Turner, a white, 41-year-old decorator who has lived in Stoneyholme for two years. "I like it here," he said. "The neighbours can't do enough for you. It's much nicer than where I used to live."

Still more to do

Yet I cannot share the view, expressed by some I spoke to, that physical segregation is nothing to worry about. Some locals did see it as a problem. A young mother in Oldham, wearing a headscarf, expressed unease at the prospect of sending her children to an unmixed school. And a 23-year-old law student in Bradford, Waqar Ali, explained to me why he regards educational desegregation as important: "If you've got a mixed community in a school, you're educating them about each other. If you're segregated, you never can educate them." Like Waqar, I find it hard to see how understanding can flourish where communities do not live and learn side by side.

It is important to stress there were signs of progress in altering this segregated reality. The Manningham Housing Association has had some success in introducing Asian families into white estates in Bradford; the Aksa Housing Association in Oldham is working hard to help Asian immigrants to learn English. This is the kind of community bridge-building that will help to erode geographic segregation over time. There is progress in education too. The Waterhead Academy in Oldham will bring together the pupils of a failing white school and a failing Asian school on the same site next year.

So how to get even more integration? And how can national and local government ease the economic problems of these towns?

Desegregation by force, it was generally agreed by all I spoke to, would be counter-productive. And the kind of lecture delivered by David Cameron in Munich in February, in which the Prime Minister promised a "muscular liberalism", was seen as a complete irrelevance. So what then? My Bradford guide, Ansar Ali, told me a story about his life that, I feel, points the way.

"I left school and started working as a 16-year-old in an ice-cream factory," he said. "Three weeks in, I thought: 'I can't do this for the rest of my life.' So I started a youth training scheme at Bradford council's housing department. Those individuals in my department were the first white people who I'd ever interacted with who weren't schoolteachers or officials. I was a very shy 17-year-old Asian. I had to be brought out of my shell. That's what my colleagues – all middle class, all white, from the suburbs – did. They made me the person I am today."