The Government is to relax restrictions which stop oversubscribed Catholic schools from selecting more than half their intake by reference to faith.
The move is part of wider plans to overhaul the schools system, with proposals to open new grammar schools expected in a green paper on Friday.
A No 10 source said that the admissions cap had failed in its objective of making faith schools more diverse.
“But it has prevented new Catholic schools from opening, which are more successful, more popular and more ethnically diverse than other types of state school,” the source continued.
“We’re going to change the rule, so we can allow new Catholic schools to open, while making faith schools of all kinds do more to make sure their pupils integrate with children of other backgrounds.”
A spokeswoman for the Catholic Education Service said it welcomed the Government’s proposal to remove the cap on faith-based admissions: “This will enable the Catholic Church to meet the current parental demand for thousands of new Catholic school places across the country,” she said.
The Catholic Education Service has long lobbied for a removal of the cap. Paul Goodman, executive editor of ConservativeHome, said May’s decision corrected a “burning injustice” against Catholic schools.
The cap, he suggested, was there largely because ministers were “terrified of the electoral consequences of allowing more or larger Muslim schools”.
But he argued that the policy had failed to make Jewish, Muslim, Sikh and Hindu schools more diverse because these schools were unlikely to appeal to parents of other faiths.
The rule was “effectively discriminatory” for Catholics, he said. Quoting another author on the site, he explained: “It prevents them from opening new free schools because it is almost certainly against canon law for a Catholic bishop to set up a school that turned away Catholic pupils on the basis of their Catholicism”.
On Wednesday, Prime Minister Theresa May told Conservative MPs she wanted “an element of selection” in the education system, but that new grammar schools would not be forced on areas that did not want them.
Justine Greening, the Education Secretary, said when answering questions in the Commons that she recognised the debate over grammar schools was “emotive”, but that forthcoming policy was “absolutely not about going back to the past”.
The Conservative 2015 manifesto promised to “allow all good schools to expand, whether they are maintained schools, academies, faith schools or grammar schools”.