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
A One Direction fan said she was delighted after Harry Styles grabbed her posted during a concert and corrected her grammar.
John Inge, the Bishop of Worcester, says the death of his wife from cancer at the age of 51 has set him in opposition to the legislation.
A cool weekend ahead but looking dry for many with sunny spells.