Ofsted inspectors found that pupils at a private London Muslim school were not able to tell the difference between Sharia law and English law.
Inspectors concluded that young people at Mazahirul Uloom School in Tower Hamlets were being taught a narrow curriculum regularly focusing only on the Islamic faith and culture.
Many pupils told Ofsted that learning about other religions was wrong.
Some pupils told the watchdog that it was a woman's job to "stay at home and clean and look after the children", while others, when talking about Sharia law and English law, were unable to say which laws they should follow and which were more important.
Ofsted said pupils at the schools may be vulnerable to extremist influences
The report, in which the watchdog concluded that children were not being prepared for life in a "diverse British society", is one of seven published on schools in the east London borough, including one state school - Sir John Cass Foundation and Redcoat Church of England School - and six independent schools, all of which have links to Islam.
The independent schools are Mazahirul Uloom School, Ebrahim Academy, East London Islamic School, London East Academy, Al-Mizan School and Jamiatul Ummah School.
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Ofsted's chief Sir Michael Wilshaw said pupils at the independent schools inspected may be "vulnerable to extremist influences and radicalisation."
In the report he wrote: "I am extremely concerned about the large number of failings in each of the six independent schools inspected.
"I am not convinced that the leaders of these schools have sufficient capacity to bring about the necessary improvements to safeguarding, the curriculum and the quality of teaching and learning.
"I believe that, in all six schools, pupils' physical and educational welfare is at serious risk."
The report into state school Sir John Cass found that leaders had organised separate boys' and girls' entrances and exits, and there were segregated outdoor and indoor spaces at break and lunchtimes.
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It also said that the school had not responded appropriately to police concerns about a social media website bearing the name of a school sixth-form society which had links to individuals associated with extremism.
Education Secretary Nicky Morgan called for urgent action from the schools following the Ofsted reports.
She said that the government had the right to close the schools involved if improvements were not made within weeks.