IT IS known as the Trojan Horse plot, but it may have been less subtle. Late in 2013 an anonymous letter was uncovered, outlining a hardline Muslim plan to “overthrow” teachers and governors in several Birmingham state schools and replace them with people who would run the schools on orthodox Islamic lines. The furore has grown, eventually involving Peter Clarke, once the head of counter-terrorism in London’s Metropolitan Police, who will lead a government investigation.

The letter may be a fake, but something has certainly gone wrong in Birmingham’s schools. Leaked reports about several academies (schools that are state-funded but independently run) by Ofsted, the schools inspectorate, suggest that in some classrooms boys and girls are seated apart, that sex education is ignored and the theory of evolution dismissed. Ofsted is investigating 25 schools in the city. This is more than a local problem, because it hints at flaws in England’s otherwise rather commendable education reforms. What has gone wrong in Birmingham is related to what has gone right elsewhere.

The last, Labour, government set some schools free from control by local authorities, which had often run them shoddily. The Conservative-Liberal Democrat coalition that has run Britain since 2010 has gone much further. About 60% of secondary schools are now independent academies. A further 173 are “free schools”, never under local-government control. Parents and local business folk have been encouraged to become more involved in running schools. So too have religious groups.

Their influence is both formal and informal. Formally, Anglicans, Catholics and Jews, who have long run state schools, are being joined by others. Between 2011 and 2013 there were 831 applications to open free schools. The British Humanist Association, a secular outfit, has identified the religious affiliation—or lack thereof—of 659 of the applicants. They include 32 linked to the Church of England, almost half of which were approved. Fully 80 Muslim groups applied to run schools, although just five were granted approval (none of the schools under review in Birmingham is a religious school).

Informally, Muslim parents are becoming more involved in schools of all sorts. In the London borough of Tower Hamlets, the Collective of Bangladeshi School Governors encourages it. Ibrahim Mogra, a Leicester imam who has served as a governor in several schools, says there is a place for faith schools, as long as they teach the national curriculum and abide by the law. But in areas with large Muslim populations, he argues that secular state schools can serve pupils just as well if parents keep in touch with teachers to ensure that the curriculum is taught in a way that does not cause anxiety.

Much of this is to the good. Bangladeshis’ exam results have improved so dramatically in recent years that they now outscore whites in GCSE exams taken at 16—astonishing for a mostly working-class group. But there have been calamities, too. An explicitly Muslim free secondary school in Derby was closed earlier this year following criticism of poor education standards and discrimination towards female staff. Muslim schools are trickier to handle than Anglican or Catholic ones, because British Islam varies so much in interpretation. Without clear structures of central authority, schools vary, and zealots can spy an opportunity to take over.

The Birmingham affair has also highlighted gaps in the inspection regime. The Department for Education is responsible for free schools and academies, but as their numbers soar it is increasingly hard to keep track of what is going on in them. Sir Michael Wilshaw, Ofsted’s head, has argued that as schools become more autonomous some kind of stronger local oversight is needed, so that problems can be caught and dealt with more quickly.

Even if that happens, the difficulty of running any kind of religiously inspired school in an increasingly secular country grows. Politicians have smiled on faith schools. Many do not. A poll last year by YouGov put popular support for state funding of religious schools at just 32%.

Clarification: Editorial constraints meant we did not represent Mr Mogra's comments perfectly accurately in the original version. We quoted him saying religious schools are unnecessary. We have amended the story to reflect more precisely what he said.