One in ten Church of England dioceses has called on its faith schools to move away from selecting pupils by faith. But there is still a long way to go to make admissions in oversubscribed schools fairer, campaigners say.

New findings from the Accord Coalition, which advocates inclusive education, show that four of the 42 dioceses, Oxford, Lincoln, Leicester and Southwark, advocate that over-subscribed schools should not select pupils on religious grounds.

In addition, the London and Chichester dioceses have recommended that new schools should not select by faith.

London, where currently nearly seven in ten places in its 18 secondary schools are allocated by faith, goes even further and recommends that its existing schools do not select more than half of pupils on religious grounds.

The Chester diocese recommends its schools should admit some children without recourse to faith, but does not specify a limit.

In spite of the changes, however, campaigners say there is still a gap between the aims of most dioceses to be inclusive and what is happening on the ground.

Chair of the Accord Coalition, Dr Jonathan Romain, said: "Many Anglican schools have yet to act on the more inclusive policies being advocated by their own diocese, so we welcome the new direction, but urge that its implementation be speeded up. Church authorities should demonstrate their words will be followed by action."

Rev Stephen Terry, who co-organised an open letter published at Easter from 20 members of the Church calling for its schools to move away from selecting pupils by faith, said: "Church of England schools should be inclusive, as an expression of the warmth and generosity of the Church's mission to the whole community. The lead being provided by these Dioceses should be encouraged and supported.

"In 2013 the Archbishop of Canterbury, Justin Welby, said that it was not necessary to select by faith to get a really good school. The inclusive approaches of the dioceses reaffirm his point and should motivate local schools to change, and inspire others throughout the country."

Last year the new Chief Education Officer of the Church of England, Rev Nigel Genders, indicated that many new Church of England schools would be fully inclusive in their admissions policies.

The Fair Admissions Campaign investigated the claim and found a mixture of approaches being pursued. Recently opened schools include the Green School for Boys in Hounslow, St Mary's Church of England Primary School in Ealing and Fulham Boys School, all in the London diocese, and the the King's School in Hove, in the Chichester. All five schools have opted to select up to half of pupils by faith in their oversubscription criteria - despite both dioceses stating they want new schools not to select on faith grounds.

Almost all pupil places at state funded Methodist schools and all places at state funded United Reformed Church schools are given on a non-faith basis.

While the four secondary schools in the Leicester diocese have become almost entirely open, selecting just 3.4 per cent of pupils on faith grounds, there is still a mismatch between the stated aims of the other dioceses and reality.

Lincoln has four secondary schools and more than six in ten places are allocated by faith. Southwark has 13, and nearly six in ten places are faith-based. At Chichester, more than half the places in its nine Church of England schools are allocated by faith. In Oxford, about a fifth of places in its 11 CofE schools are faith admissions.

A church spokesman said: "Accord are confusing the requirement of a school governing body to have regard to diocesan advice with the fact that the governing body is the admissions authority and solely responsible for setting its over-subscription criteria in accordance with the admissions code. Whilst dioceses rightly offer advice, the governing body is best placed to understand the nuances of its local context and set admissions criteria accordingly."