Around one in six schools are continuing to flout the government's admissions code, designed to ensure poorer pupils can access the best state school places, it is estimated.
A report into schools in Manchester, Northamptonshire and Barnet found one in six state schools, the vast majority of which were state schools, were breaking the admissions code.
Schools secretary Ed Balls admitted there was no reason to suppose the situation was not mirrored across the country.
However, Mr Balls was accused of conducting a "witch hunt" after naming and shaming the worst offending schools.
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Highlighted in the findings were six schools, five Jewish and one Church of England, that required parents to make a voluntary donation on admission.
One Jewish school in north London was asking parents for £895 a term.
Mr Balls said parents would not see this as voluntary and the practice was inconsistent with state education.
However, Mr Balls was accused of failing to appreciate that faith schools use the money to fund additional religious education not included in the national curriculum, as well as specialist security.
Of the 96 schools breaking the admissions code, 29 schools were failing to comply with at least two requirements.
The most frequent abuses were schools failing to give priority to children in care or refusing to take pupils with special needs.
Schools were also criticised for selection by gender, asking questions about pupils' background, given places past on grandparent's past attendance or giving priority to the children of employees.
Of the 87 faith schools breaching the code, 42 were Church of England, 32 Catholic and 13 Jewish.
The Liberal Democrats said parents would be "rightly enraged" by some of the tactics employed and it was unacceptable for any school to break the admissions code.
The Lib Dem schools spokesman David Laws said: "The backdoor power of selection from schools such as specialist schools should be removed and the government must concentrate on making every school a good one."
But he warned the government not to single out the schools to distract from the wider problems in the admissions system.
Shadow schools secretary Michael Gove accused Mr Balls of conducting a witch hunt and said there was no evidence the "voluntary donations" had determined admissions.
Mr Gove said: "Ed Balls knows that many faith, and other, schools ask parents if they'd like to make purely voluntary contributions. He also knows that Jewish faith schools have to secure additional funding to guarantee the physical safety of their children.
"But he put these schools in the dock simply in order to distract attention from the fact that 100,000 parents weren't getting their first choice of school thanks to his policies."