A new generation of free schools pioneered by Michael Gove has turned into a "dangerous ideological experiment" that has run out of control in light of the row over al-Madinah school in Derby, Tristram Hunt has warned.

The new shadow education secretary has written to Gove on the eve of an Ofsted report about the Islamic faith free school, which faces the threat of closure after it was accused of forcing female teachers to wear headscarves. There were also reports that it segregated pupils.

The school was forced to close on a temporary basis during the Ofsted inspection earlier this month but later reopened. The inspection followed claims by a teacher, who had resigned from the school, that female staff were obliged to follow Islamic dress codes. Pupils were also segregated in classrooms, with girls sitting at the back.

Hunt believes al-Madinah highlights one of the central flaws in Gove's free schools initiative – that there is minimal oversight.

In his letter to Gove, Hunt writes: "I know that you will be concerned as I am that one of your free schools has failed to provide the quality of education we should expect for our children. In this school, as well as others across the country, your policy is being exposed as a dangerous ideological experiment which has been allowed to run completely out of control."

Hunt said over the weekend that he supported the right of parents, teachers and social entrepreneurs to set up schools. But he said Labour's parent-led academies would be different in three key respects: the new academies would open only in areas where there was a shortage of school places; they would have to employ properly qualified teachers; and there would be proper systems of financial accountability and transparency.

In an interview on the Andrew Marr Show on BBC1, Hunt said al-Madinah free school showed the danger of not adopting such a framework. He said: "What is going on with the al-Madinah school in Derby is a terrifying example of the mistakes of Michael Gove's education policy. You have a system which allows essentially financial irregularities, allegations of extremist curriculum, teaching ideas contrary to British values because there is no oversight there."

Lord Nash, the education minister, wrote to the school less than a week after the Ofsted inspection to say that he would be forced to terminate the school's funding agreement unless "swift action" was taken to address a series of concerns. Nash said the school had "manifestly breached" the agreement by failing to ensure the safety of children, delivering poor standards of education and discriminating in its procedures towards female staff.

In his letter, Hunt says: "Given that prior to the opening of al-Madinah free school you received a number of warnings from Ofsted regarding potential issues with the welfare, health and safety of pupils, what steps were taken to ensure that these warnings were heeded and that all issues were resolved before the school opened?

"Given that a senior Department for Education spokesman was quoted over the weekend as suggesting that you 'always said some free schools would fail', can you please explain how you will provide parents with a firm guarantee that their children's education and safety is not being put at risk due to the inadequate oversight of your free schools programme?