There have been "concerted efforts" to run a small number of Birmingham schools in line with strict Islamic principles, headteachers said.
The National Association of Head Teachers (NAHT) said it has concerns about actions within six primary and secondary schools in the city.
Members also expressed concerns that school leaders were pressured to adopt certain philosophies and staff were being appointed on their religious beliefs rather than their skills, according the union's general secretary Russell Hobby.
He added that there are fears some youngsters are not getting their "basic entitlement" to a rounded education.
The warning comes as inquiries by several bodies, including West Midlands Police, the Government and Ofsted, continue into allegations of a hardline Muslim takeover plot at a number of Birmingham's schools.