The former chief Rabbi Lord Jonathan Sacks once likened this country's infatuation with multiculturalism to permanently living in a hotel. We may live in one place but we occupy separate rooms, sharpening our divisions while weakening our collective national identity.

The summer of 2001 witnessed the cost of this decades-long aggrandising of ethnic identities.

First came the riots in northern mill towns between young Asians and white British. Marking out territory as "ours" and "theirs" was a key stimulus.

Then came 9/11. Polls exposed the gulf between a significant minority of British Muslims and the rest: 9/11 was justified, Mossad was behind it, death was appropriate for those who insult Islam.

As 2001 drew to a close, Professor Ted Cantle, a leading authority on intercultural relations, warned we risked separating communities into their parallel lives. In 2005, following 7/7, Trevor Phillips, then head of the Equalities and Human Rights Commission, warned we were sleepwalking into segregation.

Jews have always shown a need to take their place in a wider society

None of this prevented the authorities from turning a blind eye to 1,400 young white women in Rotherham being handed over to sexual predators, disproportionately of Pakistani heritage. Political correctness - fear of being labelled a "bad" (ie racist) person - contributed to this silence.

Anne Cryer, the former Labour MP for Keighley, knows better than most what that feels like - even though her grandchildren are half Indian and African. "When you are in a room full of Asian people who are shouting you down, it does get very frightening and very upsetting," she says. "I can understand people being put off from raising these issues." Even some in her own party shunned her. No one, she says, should "diminish the power
of what it feels like to be called
racist when you know you aren't".

Political correctness may also have inhibited the police in Tower Hamlets, east London, from investigating with sufficient rigour allegations that Britain's first directly elected Asian mayor, Lutfur Rahman, cheated his way to re-election in 2014. Some politicians, including the odd Conservative, remain in denial over the bigotry to which Muslim children were exposed in those Birmingham state schools that were part of the "Trojan Horse" plot.

And yet promoting integration has become the shared aspiration of all major political parties. They talk endlessly about the importance of "social cohesion". The problem is that they talk in grand generalities.

The national conversation over how to forge a common life between Britain's very diverse and rapidly expanding ethnic minorities and everyone else has been conducted in an absence of hard empirical data about what's actually happening on the ground.

Last week, the think tank Demos tried to rectify that by launching its "integration hub" website, which has pulled together all the available data on minorities: where they live, their work and welfare, social and everyday life, education and attitudes and identity, and - crucially - how they interact with the majority white British.

Funded mainly by the Home Office, this work has been championed by former Director of Demos David Goodhart, whose book The British Dream brilliantly captures with crunchy facts and anecdotes Britain's post-war transformation by immigration. Of the world's 7 billion population, some 400 million (nearly 6%) are now living and working outside their country of birth. Here's how this migrant tidal force is changing Britain:

● The BME (black and minority ethnic) population of England and Wales is now some 10 million - up a hundredfold since 1951 when it was 100,000.

● Fewer than half of London's population is now white British. The capital's overall white-BME ratio is 55:45 - roughly where some demographers think most of the country will be in another 50 years

The Demos Hub's stand-out statistic, however, signals a growing separation between ethnic minorities and whites. Around 41 per cent (4.1 million) of the BME population now live in wards where the population is less than half white. This compares with 2001 when 25 per cent (1 million) of the BME population was living in "minority-majority" wards.

This is happening because ethnic minorities have been moving from their traditional areas of concentration into super diverse areas - eg Bangladeshis moving from Tower Hamlets to neighbouring Redbridge. At the same time whites have been moving away from these areas into whiter ones.

So, while ethnic minorities are becoming less segregated from each other, whites are becoming more segregated from them.

It's not yet possible to measure the impact of this BME-white segregationist trend, partly because the record levels of immigration sustained since 1998 means that minority communities are being constantly replenished.

Moreover, integration is a difficult concept to measure objectively, not least because it means different things to different people.

To Demos it means "convergence in life chances and to a lesser extent in lived experience between the largest ethnic groups".

Goodhart cautions that this doesn't mean everyone should be converging on the values or lifestyle norms set by the white British majority. But we should start to worry "if certain groups are diverging too far" from each other - especially in economic life and education because upward mobility for minorities is tougher if they aren't connected to mainstream networks. Also, for trust to transcend ethnic boundaries, there needs to be a degree of cultural commonality.

In practice a well integrated society is one where both ethnic minorities and the majority converge by adapting to one another such that "habits and preferences are no longer correlated with race and ethnicity", as Trevor Phillips, the Integration Hub Chair, puts it.

On the other hand, too much convergence and you get assimilation - something that most ethnic minorities, including Jews, have held out against. And, just because an ethnic minority is integrated doesn't necessarily end in a success story. Many Caribbean men have married white women but socially and economically this has been pretty disastrous, with 61% of these marriages ending in single-parent families.

The data emerging from the Demos Hub shows us what a complex business integration is - and how little we have drilled down into its detail.

So where does the line of convergence ideally lie? The story of how Britain's oldest religious minority transitioned from migrants dismissed as alien to the mainstream of Britain's cultural economic and political life offers the answer.

Today, Jews still concentrate in certain suburbs, so residentially remain largely separate. They also remain distinctly Jewish in other ways - some 60 percent of school-age Jewish children attend Jewish schools (mostly state funded) and about 75 per cent of British Jews are affiliated to 400 synagogues where Hebrew is taught.

Yet Jews have also been determined to take their place among wider society. They did not have government welfare, nor did they wait until some council official begged them to learn English, at state expense. They took upon themselves the task of integration and have achieved an enviable rate of social mobility by prioritising education and material success. As Rabbi Sacks has said: "Jews did not seek multiculturalism. They sought to integrate, adapt and belong. Jewish schools focused on turning Jews into British citizens."

This trajectory of strong cultural retention with upward mobility is also turning Sikh, Hindu and Chinese migration into a success story, both significantly outperforming the UK population as a whole when it comes to university degrees. This has increasingly connected them to wider society beyond their cultural community in business and the professions.

As for the huge influx of white eastern Europeans, we might expect them to follow the more assimilatory trajectory of Irish migrants to Britain with intermarriage, residency and socio-economic profiles, in time mirroring the population as a whole.

If the Jewish version of separatism and Irish assimilation are the two trajectories that historically have broadly characterised integration here, where does that leave British Muslims?

Like Jews, Hindus Sikhs and the Chinese, Muslims are also determined to maintain their own culture and identity. What they don't yet seem to have in sufficient vigour is the same positive attitudes towards wider society.

In Muslim communities, the much stronger sense of a separate way of life is striking not only because institutional structures like halal shops, mosques, madrassas and Islamic organisations like charities are so much more obvious but also because they are much more numerous. And without more interaction with wider society, monocultural schools reinforce this separateness.

The greatest challenge to a settled line of convergence is posed by Pakistanis, Bangladeshis and Somalis. According to the Muslim Council of Britain, the proportion of Muslims who have never worked is almost five times the rest of the population, resulting in much lower household incomes. Largely explained by purdah (banning female contact with unrelated men), low income and poor English remain major barriers to social mobility for Muslims, although there have been advances in some Muslim work rates and degree attainment.

At the same time, religious identity for Muslims is growing rapidly while for Christianity it's dying. By 2050, although Christianity will still be Britain's largest religious block, it will no longer represent most Britons. Islam is already the second largest faith block in Britain and far outnumbers Hindus, Sikhs, Buddhists and Jews combined. Therefore the number of segregated Muslim neighbourhoods seems likely to grow.

Preventing a balkanised Britain is perhaps the single most important public policy issue of the day. The Demos Hub should help us meet this challenge by generating a constructive conversation, free from bogus charges of racism and Islamophobia, informed by evidence and facts - and with the Jewish story of integration, emulated by Sikhs and Hindus especially, acting as a light to this fast-changing nation.