A survey involving 1,000 members of the Association of School and College Leaders (ASCL) found that 24 per cent were opposed to the idea, while 67 per cent felt strongly opposed.
The reform was announced by education secretary Nicky Morgan in June and is to apply to pupils starting secondary school this month. It means they will have to study English, maths, science, history or geography, and a language up to GCSE level.
Concerns raised by respondents include not having enough room for creative and vocational subjects and that the EBacc would not "suit the needs" of every pupil.
Three-quarters of the school leaders, however, said they would be more likely to back the idea if there was more flexibility in the choice of subjects.
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