Labour is calling for cross-party talks on how religious education is conducted and monitored in the state sector as a special poll for the Observer shows widespread concerns about the use of taxpayers' money to fund faith schools in a multicultural Britain.

The survey by Opinium shows that 58% of voters now believe faith schools, which can give priority to applications from pupils of their faith and are free to teach only about their own religion, should not be funded by the state or should be abolished.

Of those with concerns, 70% said the taxpayer should not be funding the promotion of religion in schools, 60% said such schools promoted division and segregation, and 41% said they were contrary to the promotion of a multicultural society. Fewer than one in three (30%) said they had no objections to faith schools being funded by the state.

Labour supports the continuation of state-funded faith schools and shadow education secretary Tristram Hunt said he saw them as "an important part of the educational landscape". But he said the recent controversy in Birmingham, where six non-faith schools have been put into special measures and a further five criticised following allegations of a plot by hardline Muslims to infiltrate them, had raised important questions about the relationship between education and religion in a multicultural society.

Acknowledging that none of the schools criticised by Ofsted had been faith schools, Hunt said the row had triggered a real debate which politicians needed to join. "Events in Birmingham have raised questions about faith, multiculturalism and state education and in the aftermath this is the moment to think about discussing, on a cross-party basis, how we manage potential tensions, particularly in urban districts."

Hunt said he believed that in future Ofsted should have a strong role in inspecting how religion was taught in faith schools, and that only qualified teachers should give instruction on the subject. He suggested that schools should teach about other religions, and not just one.

Opinium found that 75% of the public believed there was a serious risk pupils could be encouraged to adopt extremist views in predominantly Muslim schools. A majority – 56% – thought all faith schools should have to teach the national curriculum rather than being free to teach only about their own religion.

There are currently 6,844 state faith schools – a few more than in early 2010, before the coalition government came to office, when there were 6,832. Of these, 4,601 are Church of England, 1,986 Roman Catholic, 26 Methodist, 152 of other Christian faiths, 48 Jewish, 18 Muslim and eight Sikh; and 763 of these faith schools are academies or free schools.

Senior Church of England figures put up a robust defence of faith schools and said no one could credibly argue that C of E schools "which account for the overwhelming majority of faith schools in this country are hotbeds of doctrinal radicalisation or extremism".

The Rev Jan Ainsworth, the church's chief education officer, said: "Church schools continue to be hugely popular with parents, who as taxpayers are part of the public funding for education. The church itself puts a considerable amount of time and money into its schools, maintaining the land and buildings, providing 22,000 governors and a diocesan umbrella structure which with the demise of the local authority is sometimes the only support left to schools. Church schools are not divisive but provide an inclusive education, open to pupils of all faiths and none."

But Rabbi Jonathan Romain, chair of the Accord Coalition (which campaigns for inclusive education), said faith schools could be "divisive" and risked fostering "educational apartheid" where children of different faiths were ostensibly "ghettoised". He said: "They can limit the horizons of the children by focusing on faith to the exclusion of other areas; schools should be about education, not indoctrination."

Romain, minister of Maidenhead synagogue, added: "It's a discrimination not tolerated in any other area of the public sector, yet we legally allow it in schools."

Haras Rafiq, of the counter-extremism thinktank Quilliam Foundation, said: "Private faith schools can work, but it depends on what interpretation of faith they are teaching. If it is one that promotes pluralism, respect, acceptance of all in a democratic society – they can have a positive effect. If, however, an extremist narrative is being indoctrinated into young minds, this can be problematic."

Ibrahim Mogra, assistant secretary general of the Muslim Council of Britain, said: "It's a very British thing to have faith schools as part of the education system in this country. As far as I know, faith communities started things off on their own without any government help or assistance. Communities have chipped in themselves until such a point when the government of the day decided that some schools would be funded by the state.

"Parental choice is a cornerstone of our education system; families and parents having a school which has a faith-based ethos is one of the choices they opt for, and that should be available.

"Those schools should be run by the book, national curriculum subjects should be taught, mandatory subjects must be of the highest standard and families should be free to choose. Of course, whichever school is found to be teaching anything illegal should be taken to task."

Julian Bond of the Christian Muslim Forum, which promotes faith as a catalyst for good relations, said that faith schools were very popular with "Christians, non-Christians and Muslims and people of other faiths."

He added: "We are very positive about faith being recognised and included [in the education system]. Even Richard Dawkins talks about the importance of Christian heritage to this country."