The Office for Standards in Education, or OFSTED, said five of 21 schools it inspected in the central English city of Birmingham failed to protect students from extremism.
The inspections were spurred by an anonymous letter alleging a plot called "Operation Trojan Horse" by hardline Muslims to infiltrate Birmingham schools.
Authorities believe the letter was a hoax, but the alleged plot has inflamed tensions in Britain's second-largest city and sparked a public feud between senior government ministers over the best way to confront extremist ideas.
Inspectors said governors tried inappropriately to influence the curriculum at some schools, promoting a "narrow faith-based ideology" and in one case attempting to ban mixed-sex swimming lessons.
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"Staff and some head teachers variously described feeling 'intimidated', 'undermined' or 'bullied' by governors, and sometimes by senior staff, into making changes they did not support," Wilshaw said.
Of the schools inspected by OFSTED, five were classed as failing and placed under special measures, 12 were told they needed to make improvements and three were praised.
Vice chairman David Hughes said the inspectors "came to our schools looking for extremism, looking for segregation, looking for proof that our children have religion forced upon them as part of an Islamic plot."
"The OFSTED reports find absolutely no evidence of this because this is categorically not what is happening at our schools," he said.