Labour's shadow education secretary has blamed the Trojan Horse schools scandal on lack of accountability and oversight of academies - but he is not planning to put them back under council control.

Instead Tristram Hunt, in an exclusive interview with the Birmingham Post, said his party would introduce a new tier of school 'directors' with the power to investigate issues raised by parents and teachers.

Mr Hunt also warned that the problems exposed in Birmingham schools by the Trojan Horse affair have not gone away.

But they are not limited to Birmingham, nor to Muslim communities, he said.

Labour's education spokesman insisted there could be no room in schools for religious ideologies which treat girls as second-class pupils or fail to ensure every child is equipped for the modern world.

Related: Improving vocational education a priority for Labour - Hunt

He said problems in Birmingham schools were partly caused by a lack of accountability, particularly in academy schools which report directly to the Department for Education – effectively giving worried parents and teachers nobody to report their concerns to.

Mr Hunt, the MP for Stoke-on-Trent Central in Staffordshire, has been Labour's education spokesman since October 2013.

In that time he's upset independent schools, warning that they would lose their charitable status unless they shared facilities with the state sector, and seen off Michael Gove, the Conservative Education Secretary who was moved to a different post in 2014.

He was also consistent in demanding action to protect Birmingham pupils following claims there had been an organised attempt to introduce an Islamist ethos into several schools in the city.

The plot was named "Trojan Horse" in a letter and later inquiries by Birmingham City Council and the Department for Education found there had been "co-ordinated, deliberate and sustained action, carried out by a number of associated individuals, to introduce an intolerant and aggressive Islamic ethos into a few schools in Birmingham".

Interviewed at Westminster, Mr Hunt warned: "There is still cause for concern. I think the spotlight on Birmingham has helped to address it but I don't think it's gone away as an issue."

One of the problems facing city schools was a lack of accountability, particularly because some had been academies which the city council had very little influence over, he said.

"Where could you go if you had concerns about the governance of your school? In an academy there's basically nothing between the chairman of governors and the Secretary of State. There's this huge space in between, and so the concerns that some parents and some teachers were beginning to have about what was taking place in Birmingham, there was no middle tier."

Labour's plan to create school directors covering multiple authorities would provide "that middle tier which has the capacity to ask questions, to intervene, to challenge and to highlight difficulties," he said.

But Mr Hunt also warned there was a "broader issue" about the extent to which parents could expect their beliefs to be embraced by schools.

"In an era where people's religious and cultural identity is very important, where parents want to be involved in the education of their children, how can we balance that with the broader function of schools in terms of teaching citizenship and broader civic values, and a more coherent sense of citizenship?"

He said there was a role for religious faith in schools – but not at the expense of equality and a rounded education.

"To my mind, even if it is a faith school you can't have boys at the front and girls at the back. If it is a faith school and the British taxpayer is paying, there are certain fundamental standards that have to be dealt with."

He added: "In some of our inner cities the challenge is not necessarily an absence of understanding of faith, it's a need to ensure children are being prepared for the modern world and literacy and numeracy standards are where they need to be."

Birmingham was not alone in facing problems, he said, highlighting similar concerns which had been raised in Bradford. And he added: "This isn't unique to the Muslim community," pointing out that exam watchdogs had been forced to act when it emerged an ultra-Orthodox Jewish school in London had blanked out questions about evolution on a GCSE paper.

Mr Hunt also spoke about Birmingham's troubled Children's Services department, criticised by Ofsted last year for "widespread and serious failures", but warned the number of commissioners and advisers sent in to deal with the problems might be counterproductive.

They include Lord Warner, appointed by the Education Secretary, and Sir Bob Kerslake, appointed by the Local Government Secretary to look into corporate governance across the authority.

Mr Hunt said: "I think we probably need some clarity in the multiple layers."

He had confidence in the ability of the council to improve the service, he said, and praised Brigid Jones, the council's Cabinet Member for Children and Family Services.

"Birmingham on one hand is a remarkable success story. More and more people are coming there, it's feeling confident, it's growing, the prosperity is moving in the right direction.

"But you do have real challenges in terms of the local authority capacity for children and young services. I have a lot of faith in the council lead on children and young people, I think she's doing a really good strong job.

"So I wouldn't want to pronounce from London on whether they can do it or not. I think they have a lot more work to do."