Michael Gove has supported a cap on Catholic pupils at a new school due to be opened, despite other faith schools existing with no intake limit.
Current legislation, recently introduced by the Department for Education (DfE), means new faith free schools and academies have to limit the intake of faith pupils to 50% if they are oversubscribed.
But as the proposed plan is for a voluntary-aided school, which will be in Twickenham, the school does not adhere to the new laws.
In his reply to Cable, Gove wrote: "The school will be able to admit pupils on the grounds of faith, but the 50% non-faith provision for the schools admissions will not apply," the BBC reported.
"The suggestion that the school takes on a similar position voluntarily seems very sensible to me, and I would welcome such a move."
Voluntary aided schools are mainly religious institutions, although anyone can apply. School buildings and land are normally owned by charities or religious organisations and the governing body employs staff and sets admissions criteria.
Similarly, free schools and academies are autonomous from the local authority but the 50% pupil faith cap applies.
The issue of faith playing a role in education has been in the limelight numerous times this year alone.
Earlier this month, the Church of England complained religious education (RE) was being sidelined by the government's reforms, while in February a new all-party parliamentary group was created to protect RE.
A DfE spokesperson said:
“It has long been the case that Voluntary Aided schools can recruit up to 100% of their pupils on the grounds of faith, where the school receives more applications than it has places, and there are absolutely no plans to change that.
"In the case of the new VA school proposed in Richmond, its composition is entirely a matter for the LA and the Diocese, and we would not seek to influence that decision in any way."