Only a fifth (21%) felt that free schools should not have to follow the national curriculum, the survey for Channel 4 News found.
The programme revealed the poll results as it emerged that another free school, in Bradford, is in trouble.
While 81% of people agreed that it should be compulsory for free schools to employ qualified teachers, three quarters (75%) agreed that qualifications do not necessarily guarantee a good standard of teaching.
More top news
More than half (57%) of children who smoked regularly bought their cigarettes in shops before their display was banned in shops in the UK in
The British Social Attitudes survey found a majority now supported a policy of increased spending on health and education.
Durham force already using it to predict when criminals will re-offend.