The intervention comes as Catholic and Anglican bishops express grave concern about the Conservatives' election promise of more academic selection.
The churches, which own up to one-third of state-run schools, are emerging as the loudest advocates of a return to consensus politics.
Earlier this week, the Council of Churches for Britain and Ireland condemned all the manifestos for playing down unemployment and associated poverty.
In his foreword to the new Catholic report, A Struggle for Excellence - Catholic Secondary Schools in Urban Poverty Areas, Bishop David Konstant, chair of the Catholic Education Service (CES), writes: "If schools in the poorer areas of the country are not able to offer pupils an education similar to that offered in more affluent areas, we will inevitably pass on the legacy of a divided society to the next generation. It is imperative that, as a society, we do not leave them alone in that struggle."
The report uses figures from the Office for Standards in Education that show a clear link between poverty and educational failure.
It demands better funding for schools in urban poverty areas, and fairer league tables which take value-added analyses into account.
"In an atmosphere of unrestrained competition the gap between schools in a more affluent areas will tend to grow," it says.
Representatives from both denominations this week criticised moves towards greater academic selection, which they regard as a threat to the ideal of community schooling.
"It is a very major concern," said Margaret Smart, director of the CES.
"I am not in favour of selection on academic grounds," said David Young, the Anglican Bishop of Ripon.
"It's going to create difficulties for those schools that are undersubscribed and have no way of joining this particular competition."
The bishop, who is also chair of the Church's Board of Education but spoke in a personal capacity, said selection could threaten the viability of rural schools.
Anxious to appear non-partisan, the Catholic Church will send schools a list of key questions for candidates from all parties. Liberal and Labour are asked whether Catholic grant-maintained schools will keep a majority of church governors.
Conservatives will be quizzed about academic selection and school transport, which is apparently threatened by greater financial freedom for schools.
"It's a threat to the future of denominational education," said Mrs Smart. And Bishop Young said: "We would want to look very sharply at the consequences of such a policy."
Meanwhile, the Archbishop of Canterbury has criticised the "utilitarian" direction of British education. He also backed the draft statement of values produced by the School Curriculum and Assessment Authority, describing it as an important step towards "a just and moral society".
Dr Carey told a conference at London University's Institute of Education this week: "It is precisely because there are many pressures to make education more utilitarian - a better bargain for UK plc - that all of us, including teachers, need to insist on a balanced and rounded concept of education.
"We want people who leave school to be good citizens and good neighbours, not just stuffed heads and effective contributors to the economy."
The Archbishop's endorsement of the national values statement comes despite traditionalist criticism that it should promote Christianity and marriage more vigorously.