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
Colo became a mother of three, grandmother of 16, great-grandmother of 12 and great-great-grandmother of three.
The district's director of homeland security has said officials are planning for 800,000 to 900,000 people to attend the ceremony.
The Supreme Court is set to decide on whether disabled travellers are legally entitled to have priority use of wheelchair spaces on buses.