This has added to the fears of a Roman Catholic bishop, who is warning that Catholic schools are in danger of being "swept aside" and converted to multi-faith academies in the name of inclusion.
The news came as the Church of England announced that it was planning to open 100 new academies, which would accept pupils of all faiths or none.
Carol White, children's services director of Calderdales, West Yorkshire, mentioned the senior official's comments in a consultation on local secondary education.
She wrote that he had confirmed that "in the interests of community cohesion, the Secretary of State is unlikely to approve single-faith proposals for an academy where this means a continuation of admissions criteria that insist on a high proportion of admissions being based on evidence of belonging to and practising a particular faith".
Leeds' Catholic diocese said it was concerned about the report. It has already launched an attack from its pulpits on the dangers of joint-faith admissions.
"There are those who do not support faith schools of any kind and some who believe that the only sort of faith school should be a joint one: a melting pot of all faiths," Bishop of Leeds, the Right Rev Arthur Roche, said in a letter read out in local churches.
"They would like to see our current provision swept aside as they advance their own agendas under the headings of 'inclusion', 'diversity' and 'equality'."
But the Department for Education and Skills insisted that Calderdale council had misunderstood its position and that academies' faith admissions depended on local circumstances.
A DfES spokesman said: "We are clear that, in general, academies should not admit more than 50 per cent of children on the basis of faith, except where the academy has replaced a school that already did so."