Education Secretary Nicky Morgan is demanding urgent action from six private Muslim schools after Ofsted raised serious concerns that pupils might have been left vulnerable to radicalisation and their welfare put "at serious risk".

She warned that the Government reserves the right to force the closure of the London schools involved if improvements are not made within weeks.

In an advice note to Ms Morgan, published as Ofsted released a series of highly-critical reports on schools in Tower Hamlets, east London, the watchdog's chief Sir Michael Wilshaw said pupils at the independent schools inspected may be "vulnerable to extremist influences and radicalisation."

In his advice note, Sir Michael said he was "extremely concerned" about the large number of failings in each of the six independent schools inspected in Tower Hamlets, east London.

In all of the schools, pupils' physical and educational welfare is "at serious risk", Sir Michael said.

Ms Morgan said: "We asked Ofsted to carry out these independent school inspections and the findings are very concerning. While there is no suggestion of a co-ordinated plot, it is clear that these schools are failing children and this is unacceptable. All schools must prepare children for life in modern Britain.

"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."

In one case, pupils at one private school were unable to tell the difference between Sharia law and English law, Ofsted found.

An emergency inspection of Mazahirul Uloom School in Tower Hamlets at the request of the Department for Education (DfE) found that youngsters were being taught a narrow curriculum which often focused only on the Islamic faith and culture.

Several students suggested to inspectors that it would be wrong to learn about other religions, the watchdog found as it concluded that children were not being prepared for life in a "diverse British society".

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 tell inspectors which laws they should follow and which were more important. Students were also given no lessons in drama, music and art.

The report is one of seven published today on schools in the east London borough, including one state school - Sir John Cass Foundation and Red Coat Church of England School - and six independent schools, which all have links to the Muslim faith.

The independent schools are Mazahirul Uloom School, Ebrahim Academy, East London Islamic School, London East Academy, Al-Mizan School and Jamiatul Ummah School.

In each case, inspectors declared the schools failing, or identified areas where the schools had failed to meet independent school standards.

Sir John Cass school, which was previously rated outstanding, has been declared failing.

The report into the state secondary school found that leaders had organised separate boys' and girls' entrances and exits, and there were segregated outdoor and indoor spaces at break time and lunchtime.

It also warned that the school had failed to respond properly to concerns raised by police about a social media website bearing the name of a school sixth-form society which had links to individuals associated with extremism.

A Tower Hamlets Council spokesman said that only one of the schools involved in today's reports - Sir John Cass - is under their control.

"When any issues in our schools do occur, we have a strong track record of intervening swiftly and successfully to address them," he said.

"As is common practice, we are working with Sir John Cass school's leadership to address the procedural issues identified and quickly return it to being an outstanding school."

The council said that it has no jurisdiction over teaching and standards at independent faith schools.

The spokesman added: "We do have responsibility for safeguarding children in the borough but our powers limit us to offering safeguarding training and advice to schools. We have repeatedly offered this assistance to independent schools locally but we cannot compel them to accept this help.

"We can - and we do - intervene when individual safeguarding issues are raised."

The council said it wanted to make it clear that there is no evidence or suggestion of an attempted Trojan Horse-style takeover plot in the borough.

Ms Morgan said that the DfE is in discussion with the local council about Sir John Cass and will be monitoring the school "very closely" to ensure that issues are tackled quickly.

A statement on behalf of the London East Academy, a selective Islamic independent secondary school for boys, and the Al-Mizan School, a selective Islamic independent primary school for boys, said both schools are "already working hard to address weaknesses identified in Ofsted's recent reports".

It added: "Both schools have enjoyed an excellent reputation to date, with a higher-than-national-average proportion of students gaining five GCSEs at grade C or above, including in English and mathematics.

"In addition, Ofsted inspectors noted that students demonstrated a mature and well-rounded approach to debating how they were living and growing up in modern Britain; and that teachers are keen for students to widen their horizons and become active members of British society."

The leaders of Jamiatul Ummah (JU) School said that they were "profoundly disappointed" by their Ofsted report, adding that the school accepts the conclusions and will be "working hard together to make the required improvements".

The statement, signed by chair of governors Hasan Mueenuddin and principal Abdur Rahman, says: "Whilst acknowledging that Ofsted has identified compliance issues that need to be addressed, the school leadership and governing body do think that, in reaching its conclusions, Ofsted has given disproportionate emphasis to certain issues which do not reflect the real characteristics of the school and has not portrayed accurately the school or given appropriate weight to the varied educational experiences, including national curriculum."

Tony Mullee, chief executive of Sir John Cass's Foundation said: "As the Sole Trustee, Sir John Cass's Foundation is greatly concerned by the recent Ofsted report for the Sir John Cass's Foundation and Red Coat Church of England Secondary School.

"We remain committed to addressing the leadership, management and safeguarding issues raised in the report and will in future weeks be assessing the necessary action to return the school to an 'outstanding' rating which it has constantly achieved in the past".