Schools involved in a so-called Trojan Horse plot attempted to cover up their activities, according to damning findings to be revealed by Ofsted on Monday.
According to the report, due to be released on Monday afternoon, some institutions had put on “hastily arranged shows of cultural inclusivity” to fool inspectors, including in one case a religious education lesson on Christianity.
David Cameron has ordered a “robust response” to the situation – but the schools at the centre of the alleged takeover plot by hard-line Muslims have rejected the education watchdog’s findings.
Park View Educational Trust, which is at the centre of the investigation, announced that its three schools - Park View Academy, Golden Hillock and Nansen Primary - have all been rated inadequate by Ofsted.
However, vice-chairman David Hughes insisted its three schools “do not tolerate or promote extremism”.
In a statement he said: “Our Ofsted inspections were ordered in a climate of suspicion, created by the hoax Trojan letter and by the anonymous unproven allegations about our schools in the media.
“Ofsted inspectors came to our schools looking for extremism, looking for segregation, looking for proof that our children have religion forced upon them as part of an Islamic plot.
"The Ofsted reports find absolutely no evidence of this because this is categorically not what is happening at our schools. Our schools do not tolerate or promote extremism of any kind. We have made a major commitment to raising all students' awareness of extremism, people who know and have worked with our schools are appalled at the way we have been misrepresented.”
He particularly criticised the representation of Park View Academy, subject to some of the most serious allegations, saying that the speed at which it has been attacked is “truly shocking”.
And he added that the Trust will be seeking to mount a legal challenge to the judgments
Ofsted could step up its use of unannounced visits as a result of the findings; it will also maintain a regular presence in the Birmingham schools involved, reporting directly to the Prime Minister and Education Secretary Michael Gove, who has been at the centre of a political storm over his handling of the situation.
He was forced to apologise to the Prime Minister after a damaging feud with Home Secretary Theresa May, whose closest aide Fiona Cunningham had to resign following a bitter round of briefings and counter-briefings about efforts to combat extremism.
Both ministers will attend a meeting with Mr Cameron and a specially-called session of the cross-government extremism task force to deal with the Birmingham allegations.
The Prime Minister said: “Protecting our children is one of the first duties of Government and that is why the issue of alleged Islamist extremism in Birmingham schools demands a robust response.
"The Education Secretary will now ask Sir Michael Wilshaw to look into allowing any school to be inspected at no notice, stopping schools having the opportunity to cover up activities which have no place in our society."
Ofsted reports into 21 schools that were triggered by the Trojan Horse allegations will be released by the watchdog, with a statement from Sir Michael, the chief inspector of schools.
Mr Gove has asked Sir Michael to look into the practicalities of making all schools subject to the possibility of no-notice inspections by Ofsted to stop the risk of future attempts to influence reports. The Education Secretary will also make a statement to MPs in the House of Commons about the Ofsted investigations.
The previous Ofsted inspections of five of the Trojan Horse schools, rated good or outstanding in 2012 and 2013 gave one or two days' notice.
But this time round, when snap inspections were carried out with less than 30 minutes’ notice, they were found to be inadequate.
Also on Monday, the Education Funding Agency (EFA), which carried out parallel investigations to Ofsted in Birmingham, will present evidence of efforts to persuade its inspectors that a wider range of religious teaching was on offer in at least one school.
Many of the key inspection findings from schools at the centre of the allegations have already been leaked to the media with at least five set to be placed in special measures.
Three schools have already broken cover to say they have been given a clean bill of health, receiving ratings of either "good" or "outstanding".
The allegations of Muslim extremism in Birmingham schools have sparked four separate investigations including by the Department for Education (DfE), Birmingham City Council and West Midlands Police.
Earlier this year an undated and unsigned letter, now widely believed to be a hoax, was leaked to the media setting out a five-point plan dubbed Operation Trojan Horse for hard-line Muslims to seize control of schools by installing friendly governors, and forcing out uncooperative headteachers.
Many in the Muslim community have expressed anger over the investigations, with staff at one of the schools inspected branding the inquiries nothing short of "a witch-hunt".
Additional reporting by Press Association