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.
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The Duke of Cambridge also laid a wreath to honour the victims before kick-off.
The mother of one of the Manchester attack victims has told of the distressing moment she found her daughter being treated after the attack.
Marjorie and Michael Cawdery, both 83, are understood to have been stabbed to death in a killing their family called "incomprehensible".