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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Ex-Spitfire pilot Allan Scott, 94, said he was told off by the Queen when he first met her in 1943 when she was just 16.
Last minute preparations are going on at the Church of St Mary Magdalene where Princess Charlotte will be christened.
Princess Charlotte is being christened on Sunday at Sandringham in Norfolk in only her second public appearance since she was born.