Michael Gove, the education secretary, was one of the key voices calling for a ban on support for non-violent extremism when it published its Prevent strategy to fight radicalisation last year.
But behind closed doors there are concerns about 118 "socially conservative" independent faith schools - the vast majority of them Muslim - where pupils may be encouraged to cut themselves off from mainstream society.
Ministers have been told they do not have "detailed information" about the religious orientation of the groups and movements behind all independent faith schools.
And officials have privately admitted that they also have no system in place to identify institutional extremism in state schools, the Daily Telegraph has learned.
They say there is also "a gap between what we think we know and what we can prove" because they cannot use undercover methods open to journalists.
From January, the Independent School Standards will require a respect for "fundamental British values" including democracy, the rule of law, individual liberty and mutual respect and tolerance of those with different faiths and beliefs.
Ofsted has not yet trained its inspectors in how to enforce such standards but it is introducing a "specialist cadre" of inspectors to look at faith schools as part of a planned "prioritised inspection programme."
However, the education department has admitted in briefings that it can only look at the "ethos" of independent schools, rather than how they are actually run.
And the department says it has failed to measure the mindset in state schools because it cannot work out how to "detect" extremism or a "baseline" to start from.
In the state sector, officials are only able to look at data where pupils are referred to a project called Channel, designed to help them move away from extremism.
But there are concerns that the measure is unreliable as some schools with problems may not have made any referrals.
Two teaching assistants in state schools have been involved in terrorism – Mohammed Sidique Khan, the leader of the July 7 bombers in Leeds, and Zahoor Iqbal, who helped a man planning to kidnap and execute a British soldier in Birmingham.
Religious schools are the fastest growing sector of independent schools with 80 new registrations a year.
Among "schools of interest" are three run by the Islamic Shaksiyah Foundation in Haringey, North London and Slough, Berks. Reports have claimed the foundation is run by senior members and activists of Hizb ut-Tahrir, an extremist political group that campaigns for an Islamic state.
The school said they had been reassured by the Department for Education that they have "no concerns about extremism in our schools" and said there was "no involvement of Hizb-ut-Tahrir activists on the board of the foundation."
Another school, the Alif Academy in Forest Gate, East London, is also on the list. The local council has raised concerns about links with Hizb ut-Tahrir.
Hasib Hikmat, the head teacher, said he was "shocked" by the allegations because the Department of Education had registered his school in 2011 and dealt with it "professionally and responsibly."
Another causing concern is the Darul Uloom school in Birmingham, associated with the missionary group Tablighi Jamaat, where an undercover documentary recorded children being taught a hardline version of Islam that criticised Hindus and Jews.
The document also mentions a proposal to set up a school attached to the Central Mosque in Rochdale, called Darul Ilm, which is also associated with Tablighi Jamaat.
Neither responded to requests for comment.
The briefing document also highlights an application to set up a private school at the Green Lanes Mosque in Birmingham, which has links to fundamentalist "salafi" Muslims in Pakistan, and where another undercover documentary filmed preachers speaking out against homosexuals and non-Muslims.
The mosque said the school would be run by a separate board of trustees who "have not engaged, or promoted any sort of extremist related activity or otherwise" and who were addressing issues raised by the DfE.
To add to the problems the education department faces, included in the list of "socially conservative" schools also those run by Orthodox Jews and the fundamentalist Christian sect the Plymouth Brethren.
A Department for Education spokesman said Ofsted inspectors would not go out specifically to look for extremism but added: "Ofsted is working to ensure all inspectors have the necessary knowledge and expertise to determine whether extremist beliefs are being promoted in a school and then to take appropriate action."
The government's counter-radicalisation strategy, called "Prevent" warned last year that some people who are supportive of terrorist groups and ideologies had "sought and sometimes gained positions in schools or in groups which work closely with young people."
The report warned that at least three separate al-Qaeda-related operations had involved people who became involved in extremism while they were at school, including July 7 and the trans-Atlantic airlines plot.
Eleven of the convictions for terrorism-related offences associated with al-Qaeda had been committed by people aged between 15 and 19, it added.
The youngest person convicted of terrorism-related offences was Hammaad Munshi, who was 15 when he was arrested carrying two small bags of ball bearings, a key component of a suicide vest, on his way home from his GCSEs at Westborough High School in Dewsbury.
The strategy also reported that a minority of independent faith schools had been "actively promoting views that are contrary to British values, such as intolerance of other cultures and gender inequality" and had "allowed extremist views to be expressed by staff, visitors or pupils."
The document said there had been concerns that madrassahs – after-school religious classes attached to mosques - were promoting a highly conservative version of Islam and spreading extremist views, particularly against non-Muslims. It estimated that 100,000 Muslim children attended such schools.
