The government's free schools programme is allowing "religious dogma" to be imposed on children, campaigners have warned.
The National Secular Society said the growing influence of faith groups could undermine the integrity of Britain's state schools, while the British Humanist Association said schools were using their new freedoms to duck out of teaching proper sex education lessons.
Their warnings come as education secretary Michael Gove came under pressure over the temporary closure of a Muslim free school in Derby.
The Al-Madinah school, which opened a year ago but closed its doors on Tuesday just hours after Ofsted began an inspection, has faced accusations of introducing strict religious practices.
There have been reports that female teachers at the school - which claims a "strong Muslim ethos" - were forced to wear hijabs even if they were not Muslim.
Other reports claimed that girl pupils were made to sit at the back of the classroom and boys at the front.
Richy Thompson, of the British Humanist Association, told HuffPost UK he was concerned about the schools' freedom to depart from the national curriculum, as well as what he said was a lack of transparency over who is applying to open new institutions.
"They can teach pretty much what they like, in terms of RE and sex education," he said.
"They can choose not to teach about things like sexual reproduction, anatomy and STIs, and can teach about abstinence until marriage if they want."
Thompson said "pseudo-scientific groups" applying to open free schools, adding: "It's a much situation than it was before, both in terms of what is being approved, and what they do once they are set up."
In February, the government confirmed that a quarter of free school applications were coming from faith-based groups.
Ministers say the policy allows schools to escape from local bureaucracy and allow groups to "innovate" and be different from the norm.
Stephen Evans, campaigns manager for the National Secular Society, added: "The new freedoms given to free schools coupled with their lack of accountability creates an ideal environment for religious groups seeking to impose religious dogma on pupils.
"The integrity of our state education system risks being undermined by the growing presence of faith groups, many of which seem more interested in religious inculcation than they are in education.
"The time has come for a serious rethink about the role of religious organisations in publicly funded education. At the very least the Government must find ways to more effectively regulate all schools with a religious character."
Ofsted's findings on the Al-Madinah school have not been finalised, but reports suggest the watchdog will judge it "inadequate", the lowest rating.
Shadow education secretary Stephen Twigg has written to Gove demanding answers.
He wrote: "This is, of course, not the first time that there have been questions surrounding your department's oversight of a free school.
"While I understand that there is an ongoing investigation, the reports concerning this school are of extreme concern to parents and the wider community.
"Given the confusion as to why the school has closed, and that pupils may be returning to the school on Monday, I would ask that these matters be clarified urgently in order to reassure the public."
A Department for Education spokesman said: "We were already investigating this school before the allegations became public.
"We discussed the problems with Ofsted and it launched an immediate inspection. We are waiting for Ofsted's final report and considering all legal options."