More than half agreed that the ending of local political control over schools had been a good thing and backed the decision by Tony Blair, the Labour leader, to send his son to an opted-out school.
The Research International survey for the Grant-Maintained Schools Foundation, also showed that the majority of teachers - even in LEA schools - supported Mr Blair's choice.
Only members of the National Union of Teachers and the National Association of Schoolmasters Union of Women Teachers were opposed to Mr Blair's decision.
In contrast, members of the National Association of Head Teachers supported it by 42 per cent to 29 per cent, and members of the Association of Teachers and Lecturers by 48 per cent to 24 per cent.
The survey, carried out in February and March, was based on 516 parents of children and 400 teachers in both LEA and GM schools.
Fifty-four per cent of parents agreed that freedom from local authority control was a "significant benefit", with only 13 per cent against. Twenty per cent of teachers in GM schools did not agree, compared with 71 per cent who did.
Only 22 per cent of parents agreed that opted-out schools had an unfair advantage, while members of the NUT and NASUWT were almost evenly split on the issue.
And Sir Robert Balchin, chairman of the Grant-Maintained Schools Foundation, said: "Opposition to GM status is crumbling even among its hardest critics. "
Andrew Turner, director of the GMSF, added: "This is an enormous vote of confidence in the independence of GM schools from the people who really count - parents."