A senior Tory peer is planning to propose a new legal duty on faith schools to admit a proportion of children of different faiths, echoing a call by Mr Cameron in his conference speech. But the Tory leader argues that it is an issue of “social responsibility” for Muslim schools to address rather than be coerced about.

Instead, Conservative peers will be given a free vote on the plan that is expected to be put forward this month by Lord Baker of Dorking, who was Education Secretary in Margaret Thatcher’s Government.

Lord Baker is understood to be preparing an amendment to place a legal duty on all faith schools to take a percentage of their intake from children of different faiths or none.

The amendment would be tabled to the Education and Inspections Bill, which allows for the establishment of trust schools but also for a new generation of faith schools, and returns to the Lords for its report stage on October 17 and 19.

Lord Baker’s proposal potentially has a wide cross-party appeal, since many Labour MPs might support the principle behind it. But the refusal of the Tory leadership to back it means that there is less chance that he will win sufficient support in the Lords.

Peers might also be reluctant to add such a controversial measure to the Bill at a late stage, since it has already cleared the Commons, where the main focus of debate for MPs was its provision for new trust schools.

During the Bill’s second reading debate in the Lords in June, Lord Baker said that faith schools should admit at least one third of pupils from other faiths as a condition of receiving state funding.

Although this would affect all faith schools, he directed his remarks at about 150 private Muslim schools that are seeking to become state-funded.

Lord Baker argued that it would be wrong to allow exclusive faith schools, saying that Church of England schools traditionally tended to be inclusive and that Roman Catholic schools were becoming more so.

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