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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During their visit, Charles and Camilla will meet local businesses and people in the city centre before joining a reception in the Guildhall
The United Kingdom is on course to leave the European Union next year.
The European Research Group chair said the chances of Brexit in Name Only have been ‘significantly reduced’.