I wrote this piece for the FT Weekend on the Trojan Horse affair, faith and the politics of education.

Some years ago, when I was working as an adviser in the Home Office, I accompanied a team of immigration officers on an early morning operation to detain migrants who had overstayed their visas. As dawn broke, we arrived at a house in northeast London where we expected to find men of Pakistani origin. Instead, we were greeted by a bleary-eyed British man of African-Caribbean descent who told us in no uncertain terms that he had lived in the area all his life and that we should get lost and leave him to his sleep. The immigration officers withdrew without complaint, muttering about their inadequate case files.

At a stretch, you might have called this a "dawn raid", albeit a hopelessly incompetent one. But throughout this past week, as they have reported the events of the so-called Trojan Horse affair – so named because of allegations that extremist Islamists were taking over Birmingham schools – serious national newspapers used the phrase to describe something very different: no-notice inspections for schools.

Think about that for a minute. "Dawn raids" are proposed for institutions that educate our children. Every word is a prejudice, wrote Nietzsche – and congealed in this use of language is a series of assumptions about two central questions for our democracy: first, how we school children from Muslim homes; and, second, how the state exercises its power in the contested and complex terrain of education politics. Somehow, we have arrived at a point where it is possible to speak in quasi-military terms of the prime minister asserting his authority, not just over his querulous cabinet colleagues but also the whole domain of schooling in a multicultural society.

It is scarcely credible that the words "dawn raid" would have been used if the schools concerned did not serve Muslim communities. As it turned out, the investigations and inspections that followed found little evidence to substantiate claims of extremist takeover. Instead, they uncovered serious flaws in governance and management, and a narrowing of the curriculum, but most of all an intensifying social conservatism.

If this constituted extremism, something similar could be found in any number of schools upholding religious convictions that clash with society's predominantly liberal values, whether Catholic, evangelical or orthodox Jewish. That the schools placed in special measures were not faith schools is beside the point. They were seeking to reflect the beliefs and practices of the communities they served, in the course of which they apparently undertook activities many of us would find unacceptable.

How, then, do we handle socially conservative expressions of faith in our school system? Until the recent past, English schools embodied a compromise carved out in the 1944 Butler Act between the state and the Anglican and Catholic churches. The government would fund and maintain schools run by these churches in return for bringing them into the fold of the state sector. This settlement endured for years but came under pressure when immigration brought new faith communities that raised claims for equal treatment for their children. These proved hard to resist, and pragmatic judgments were made that it was better to have such children educated under the aegis of the state than in private, unregulated religious schools.

The logic of this position is that we should now offer full equality to Muslim communities and allow many more Islamic faith schools. There are multiculturalist theorists who argue that we should follow precisely this path, broadening our recognition of cultural differences to include faith, and apply this to other public institutions – not just schools but also, for example, appointments to the House of Lords.

The confidence that secular modernisation would render faith obsolete in advanced democracies has proved misplaced. Unlike the US, Europe is not divided by "God, guns and gays" but it is struggling to integrate growing Muslim populations into its cultural self-understanding and democratic practices. Even impeccably liberal philosophers now talk of "post-secularism" and the need to find new ways of accommodating faith and reason in contemporary societies.

Expanding faith schools would be a mistake, however. All the evidence shows that this will foster greater segregation, not less. Equality of citizenship requires us to overcome unjust hierarchies of status, standing and esteem, not to promote the conditions in which they might flourish. The messy pragmatism of the Butler Act means that we will always have faith schools but we should seek progressively to diminish the importance of particular faiths to our children's education, whether it is in the curriculum or school admissions criteria.

This will require a different kind of political leadership from that encapsulated by the idea of no-notice school inspections ordered by 10 Downing Street. Liberal societies cannot eradicate the antagonisms that structure their politics but they can strengthen their ability to navigate them. Sometimes this is best done through judicial routes, as it was in 2006 when the House of Lords, quietly supported by the Department for Education, ruled against a girl who wanted to wear a jilbab (a long coat-like garment) to school, in contravention of its uniform codes. The ruling suited the school and the local Muslim community, and an accommodation was reached on a highly sensitive issue without recourse to public rancour.

On other matters, only democratic deliberation will suffice, since we cannot leave fundamental political questions to the judiciary. But democracy can be exercised locally, as well as nationally, and if the Trojan Horse affair proves anything, it is that the politics of education in England has become too febrile and unstable not to require institutional reform. No other advanced country governs its schools from central government without an intervening tier; nor do many grant such extensive powers over professional issues to politicians and civil servants. Instead of debating British values, we would do better to scrutinise the English state.