More than 60 parents had asked Derby City Council about moving their children out of the Al-Madinah free school before a damning Ofsted report was released, the BBC has learned.
The figures pre-date the report, which said the school was failing in all areas and was "dysfunctional".
Enquiries were made by 67 parents, with 33 making formal applications to put their children elsewhere.
The school said it accepted the findings and would use them to move on.
On Thursday, Dr Stuart Wilson, the acting head teacher, said there were serious problems at the school and accepted some of the lessons were not meeting necessary standards.
The Ofsted report said teachers at Al-Madinah were inexperienced and had not been provided with proper training and that the school required special measures.
Parent Razwana Bibiakbar said she would not be taking her child out of the school but added that it had let the pupils down.
She said: "Something has to be done [like bringing] new leadership, new team, new staff - qualified - into Al-Madinah school to run it properly.
"Why should I pull my daughter out of that school? Why can't they pull their socks up and fix everything?"
The Ofsted inspection had been due to take place by the end of the year but was prioritised following initial allegations that female teachers were obliged to wear hijabs and boys and girls were segregated.
David Cameron told BBC Radio Derby on Thursday that the Al-Madinah situation should not be used as a stick with which to beat the whole free school movement.