Six independent Muslim faith schools in London’s East End must make urgent changes or be forced to close, the education secretary, Nicky Morgan, said after Ofsted inspectors faulted them for failing to promote British values and safeguard their pupils.

According to analysis by Sir Michael Wilshaw, Ofsted’s chief inspector, six private schools in Tower Hamlets “focused intensively on developing Islamic knowledge and understanding at the expense of other important areas of the curriculum”, ignoring creative subjects such as music and art.

In one of a series of reports published by the watchdog, a primary school pupil at East London Islamic School told inspectors he believed he would “go to hell” if he participated in music or dance.

“Given the evidence gathered from these inspections, particularly in relation to the narrowness of the curriculum, I am concerned that pupils in these schools may be vulnerable to extremist influences and radicalisation,” Wilshaw said in his advice note to Morgan, published alongside the reports on the six schools.

Ofsted said that at Mazahirul Uloom School, a secondary school for boys, pupils were unable to tell inspectors which of sharia law or English law was more important. “Students presented a narrow view of the role of females in society. Some students told inspectors that ‘women stay at home and clean and look after the children. They cook and pray and wait for us to come back in from school and help with homework’,” the inspectors reported.

“While there is no suggestion of a coordinated plot, it is clear that these schools are failing children and this is unacceptable. All schools must prepare children for life in modern Britain,” Morgan said, ruling out suggestions of a “Trojan Horse 2” – a reference to an alleged extremist plot to take over schools in Birmingham earlier this year.

“We will now be demanding urgent action plans from the independent schools and expect to see improvements within weeks. If changes are not made, then we reserve the right to force the closures of the schools involved,” she said.

Ofsted also said it had uncovered evidence at Sir John Cass, a Church of England secondary school in Tower Hamlets, of girls and boys being segregated during breaks and lunchtime and of the school leadership ignoring warnings by the police that sixth-formers were using social media sites bearing the school’s name to post links “to individuals associated with extremist views and actions”. Students also appear to have posted messages discouraging students from attending school events, such as a fundraising karaoke evening.

“One posting states that any sixth-form students who attended a leavers’ party and engaged in ‘free-mixing’ or ‘listening to music’ would face ‘severe consequences later’,” inspectors noted.

“Senior staff and governors failed to inform students or parents of this serious concern. Neither was any information, education or training provided for students, staff, governors or parents.”

Sir John Cass and the six private schools – Ebrahim academy, the East London Islamic school, Jamiatul Ummah secondary, Mazahirul Uloom, London East academy and Al-Mizan primary school – were failed in the wake of snap inspections ordered by the Department for Education last month after it received evidence of concerns. Sir John Cass saw its rating downgraded from outstanding to inadequate and was placed in special measures.

Outside the East London Mosque in Whitechapel, near Al-Mizan and the London East academy schools, one woman with a son at Al-Mizan, who declined to be named, said: “I’m really confused. I know the school, but I’m just waiting to hear more. After the Ofsted report, I don’t want to say any more.”

Harun Asif, a former pupil at Jamiatul Ummah, said the report on his old school was inaccurate. “As far as I’m aware, the school never promoted any political ideology. It taught basic Islam, basic faith, fiqh [jurisprudence] and sunnah [teaching of the Prophet Muhammad], and didn’t promote any specific ideology or any other political form of Islam that the state would consider radical,” he said.

Asif studied GCSEs and A-levels at Jamiatul Ummah, and is now in his final year studying physics as an undergraduate at King’s College, London, having interned at Google. “I also went to madrassah when I was as a kid and I can compare the educations. When I went to [Jamiatul Ummah] school I was taught about all these other opinions; in the madrassah I was taught one opnion,” Asif said.

Ofsted’s inspectors criticised Jamiatul Ummah for failing to develop pupils’ understanding of “the fundamental British values of democracy, the rule of law, individual liberty and mutual respect and tolerance”.

A teaching assistant at one of the schools ridiculed Wilshaw’s assertion that the schools were preparing pupils poorly for British life. “This is east London. What do you mean, ‘not ready’? I feel that’s really patronising. Why focus on Muslims? It’s creating fear,” she said.

As well as raising concerns about teaching and curriculum, the Ofsted inspectors were highly critical of the schools’ facilities and practical safeguarding issues. At the London East Academy, parts of the building are open to members of the public, while Al Mizan had fire exits chained shut during the day.

At Jamiatul Ummah, inspectors described the school building as “shabby and dirty and in need of significant repair” and warned of hazards to pupils and staff at Ebrahim academy including “electrical sockets and switches damaged or hanging off walls”.