Government plans to shake up schools could open the door to religious extremists, teachers are warning.
MPs are drawing up alternative proposals
Teachers' unions have told MPs on a Commons committee they are against plans to create trust schools.
They say the changes would allow religious fundamentalists to take over state schools.
The government is facing a challenge over the reforms from some of its own backbenchers, who are drawing up alternative proposals.
Up to 30 MPs are reportedly ready to propose changes to the plans in parliament next week.
Under government proposals, due to be put forward in a Bill early in the new year, schools would be able to become self-governing trusts, with more freedom from local authorities and power over which pupils they admit.
The National Union of Teachers told the Commons Education Select Committee that the Schools White Paper deserved just five out of 10 for the best parts and "a lot lower" for the rest.
Mary Bousted, general secretary of the Association of Teachers and Lecturers, told MPs the plans could open the door to extremists.
"Say you have got an Exclusive Brethren set of parents who apply to set up a school. That sect says that their children don't need to learn with other pupils. Where are the checks and balances?
"What would the setting up of an extreme faith school within a trust do to the curriculum?"
The Exclusive Brethren are an evangelical Protestant Christian church whose members keep themselves separate from other people (including other Christians), because they believe the world is a place of wickedness.
Mick Brookes, general secretary of the National Association of Head Teachers, warned that the White Paper plans could lead to more segregation and sectarianism.
Speaking after the hearing, he said the only organisations with a real incentive to set up trust schools would be faith groups.
"If there are parents within faith communities who feel that their local school does not cater for their particular faith, then this White Paper certainly does open the door to set up faith schools," he said.
"If we promote segregation we may well go into increased sectarianism."
NUT general secretary Steve Sinnott said the White Paper would increase social inequalities, with children from the poorest backgrounds missing out on the best schools.
General secretary of the NASUWT Chris Keates said: "Children will fall through the net because of school admissions policies."
A spokesman for the Department for Education and Skills said the claims about extremists were "simply not true".
"We will put in place a number of safeguards in place to protect against this, including placing a duty on trust Schools to promote community cohesion and good race relations," he said.
"Trust schools are subject to the same accountability regime as all other maintained schools."
In his first day as Tory leader, David Cameron told Tony Blair his party would support the government on educational reforms.
"I want schools to control their own admissions. That's what's in the White Paper and let's see it turns into the Bill. Education is one of the public services in desperate need of reform.
"Our aim should be to make sure all schools have these freedoms."
Mr Blair told Mr Cameron they disagreed on admissions and that there would be no return to schools selecting pupils on academic ability at 11.
"It's not merely in respect of education policy we've got to agree. We've also got to agree the investment that's so necessary to back up that reform continues.
"I'm afraid your economic policy ... is to cut back investment."
Liberal Democrat education spokesman Edward Davey said: "David Cameron's total support for Blair's Education Bill leaves the Liberal Democrats as the only party prepared to challenge the free-for-all anarchy on school admissions proposed by the government."