Ofsted inspectors have found that some private faith schools are not doing enough to respect women, or people of other faiths and beliefs.
In one Muslim school, a "female governor sat out of sight of the male governors in an adjacent room".
The watchdog inspected 22 schools in England which had previously been inspected by the Bridge Schools Inspectorate.
Inspectors found that nine of these schools were inadequate.
Ofsted chief inspector Sir Michael Wilshaw has written to Education Secretary Nicky Morgan with the findings of inspections of 15 Muslim and seven Christian schools, in cities including Manchester, Coventry, Birmingham and Leicester.
Previous checks of these private faith schools had been carried out by the Bridge Schools Inspectorate (BSI), an independent inspectorate which had inspected about 50 private Muslim and Christian schools.
Independent schools do not come under the same Ofsted process as state schools, with inspections being carried out by independent agencies such as the Independent Schools Inspectorate and the School Inspection Service.
Ofsted had raised concerns about the "quality of BSI inspection" and, this autumn, Ofsted took over its inspection responsibilities.
One school in this current wave of Ofsted inspections - Manchester Islamic High School for Girls - was rated outstanding.
But Sir Michael's letter highlights a range of concerns about other schools previously inspected by BSI.
Four of the schools were assessed not to be "promoting fundamental British values". This included not promoting "mutual respect and tolerance of those with different faiths and beliefs".
There were concerns about a lack of exposure to other religions and "inappropriate" books.
At Al Ameen primary school in Birmingham, inspectors say pupils were not protected from reading "inappropriate literature about extremist, sexist or partisan views".
Inspectors said that at Darul Uloom Islamic High School in Birmingham, "the only female governor sat out of sight of the male governors in an adjacent room to the main meeting.
"As a result, she could only contribute to the meeting through a doorway. Governors told inspectors this was their usual arrangement.
"A senior HMI has pointed out to the school that this practice is unacceptable as it fails to show proper respect for women."
This school, now rated as inadequate, had been inspected by Ofsted inspectors since 2011. In October 2013, Ofsted rated it as good and described the head teacher as "forward thinking".
Ofsted says that although its own inspectors carried out a number of inspections in recent years, the school was considered to have been part of the BSI inspection system.
In Cornerstone School in Epsom, a private Christian school, Ofsted said pupils were "not given sufficient opportunities to learn about different cultures and the perspectives of others".
There were eight schools where there were safeguarding concerns, including "not paying due regard to the guidance issued in 'Keeping children safe in education', a lack of checks on staff or insufficient records on pupil attendance.
And in a further 10 cases there were concerns about schools not providing a sufficiently broad curriculum.
Sir Michael's letter to the education secretary says it should be a priority to inspect other former BSI schools.