Pupils at Muslim schools in east London are being made "vulnerable" to extremist influences and radicalisation, the education watchdog Ofsted says in a series of reports published today.

After seven inspections were carried out earlier this year on six independent Muslim and one voluntary aided Church of England school, Sir Michael Wilshaw, chief inspector of Ofsted, warned that the physical and educational welfare of pupils is at "serious risk".

The Muslim schools, all in Tower Hamlets, east London and three of them within mosques, were judged to be too focused on the teachings of Islam. At one school, pupils were ignorant of the fact that there is any difference beween British law and sharia or Islamic law.

In a letter to education secretary Nicky Morgan, Sir Michael said that in all six independent schools visited, inspectors had serious concerns over the safeguarding and welfare of pupils, pupils were not provided with an appropriately broad and balanced curriculum and teaching, achievement, leadership and management were "inadequate".

None of the six independent schools provided suitable changing facilities for physical education. Some had no showers or changing rooms. In one secondary school, students had to change for physical education in the dining hall.

Inspectors found four of the schools' buildings to be "dirty and poorly maintained". Sir Michael reports: "In one school, electrical sockets and switches were hanging off walls. In another school, stairwells were filled with broken furniture and rubbish."

Sir Michael says all schools focused intensively on developing Islamic knowledge and understanding at the expense of other important areas of the curriculum. "In one school, pupils said that it would be wrong for them to learn about other religions. In another, a Year 1 pupil said he believed that participating in music or dance was wrong."

However, teachers were judged to give teachers gave good instruction in Arabic studies, Hifz or memorisation of the Koran and Islamic studies.

Sir Michael says: "I believe that, in all six schools, pupils' physical and educational welfare is at serious risk. 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."

Four of the schools were judged inadequate. They are the Al-Mizan school, the Ebrahim Academy, the Jamiatul Ummah school and the London East Academy. Two were deemed to have failed to meet independent schools standards. They are the East London Islamic school and the Mazahirul Uloom school.

The Education Secretary warned that the schools will be shut if they fail to improve.

She 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."

In addition, the Ofsted report on the St John Cass's Foundation and Redcoat Church of England school, previously judged "outstanding", found it to be "a school that requires special measures".

The inspectors judged that senior leaders were failing to do enough to ensure that students are kept safe and evaluations of safeguarding arrangements are not thorough, with incomplete records of the checks made on staff and other adults working with pupils.

"The school has not put in place steps to ensure that students, staff and governors understand the risks posed by extremism," the report says. "The sixth form is inadequate. This is because students have not been given sufficient guidance on the dangers associated with using the internet, particularly in relation to extremist views."

Communication between school leaders and also governors about important safeguarding practices was found to be "poor".

The London diocesan board for schools said: "The issues raised by the recent inspection of Sir John Cass's Foundation and Red Coat School are of significant concern and are being addressed with the utmost urgency. It is a school's primary duty to provide a safe environment for learning. Extremism, in whatever form it takes, has no place in our society – especially not in our schools.

"Sir John Cass's Foundation and Red Coat has for many years been judged by Ofsted to be an outstanding school providing a high quality education for the local community. Social media content that used the school name was not reflective of its values or ethos. More time is now being given to educating the students about exposure to extremism, particularly online. Staff and students have already begun to undertake additional training using the Prevent programme. The governing body of the school is working hard with Tower Hamlets and the London Diocesan Board for Schools to rectify the concerns raised by Ofsted. Robust action has already taken place and the governors have produced a plan to bring about further rapid improvement."

A Tower Hamlets spokesperson said: "We note that of the seven schools mentioned in today's reports, only one is under the council's control. When any issues in our schools do occur, we have a strong track record of intervening swiftly and successfully to address them.

"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.

"As a local education authority, we have no jurisdiction whatsoever over teaching and standards at independent faith schools. 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 added: "The success of our maintained schools is well-known. They have an international reputation for excellence"

The local authority also emphasised that there is no evidence or suggestion whatsoever of an attempted takeover by extremists, as allegedly occurred in Birmingham under the so-called Trojan Horse scandal, either at Sir John Cass School or any other school in Tower Hamlets.

Sarah Baker, chair of the Tower Hamlets Local Safeguarding Children Board, said: "We will support the council and other agencies in bringing about the necessary improvements to ensure children are safeguarded.

"The Board does have some concerns about whether existing legislation gives sufficient authority for the council to take an active role in independent schools. The Board requests that Ofsted and the Department for Education consider this element carefully as part of their action plan to improve these independent schools."

The Mayor of Tower Hamlets, Lutfur Rahman, said: "The council has an international reputation for the quality of its schools and an excellent track record of helping turn around maintained schools when issues occur. I know the council will work with Sir John Cass's leadership to help it return to being outstanding. I encourage the independent schools to accept the safeguarding advice and guidance being offered by the council."