Clerics and headteachers are questioning how far the trend can go without affecting the fundamental religious purpose of Catholic schools, although they express satisfaction that parents are choosing their schools and do not want to end a policy of open access.
Councils are also calling for amendments to the 1981 legislation, a key plank in Conservative education policy that has led to overcrowded schools, rising class sizes and a return to "temporary huts". Thirty Glasgow primaries have maximum class sizes.
Teresa Gourlay, spokeswoman for the Archdiocese of St Andrews and Edinburgh and long-standing Catholic Church representative on Lothian and Edinburgh education committees, says: "The legislation was drafted in 1981 to tie the hands of local authorities. There is an unfairness there and it needs re-examination."
Pat Sweeney, head of Holy Rood High in the capital, raised the issue at the Catholic secondary heads' conference in Crieff two weeks ago. A quarter to a third of pupils at the 760-pupil secondary are non- Catholics. Six associated Catholic primaries are proving equally attractive to non-Catholic parents and are full.
In last year's intake of 210 pupils, 56 came from 30 primaries outside the designated Catholic schools, and 5-14 liaison is very difficult. The "wave of popularity" brings unforeseen problems. Placing requests from non-Catholics arrive late, and Mr Sweeney has no idea how many classes he will have in August, how many form classes there will be in the first year, how the numbers will affect practical subjects such as home economics and computing, how many pupils will have learning difficulties and, most important, how many teachers he will need.
"It is haphazard and unpredictable from year to year," Mr Sweeney said. "There could come a stage in certain areas when the whole identity of the schools could be undermined because of the intake. The school could be Catholic in name only and we would be concerned about that." Non-Catholic parents send their children for a variety of reasons, he believes. Some are pragmatic and are to do with distance and childcare arrangements, others are to do with school uniform and the values parents appear to support.
Mr Sweeney would like to restrict capacity in some way but he would not support a rigid definition of pupils eligible to attend a Catholic school. At St Margaret's Academy, Livingston, Scotland's most recently built secondary, Tony Gavin has similar concerns. In three years' time, a third of the 900 pupils will be non-Catholic. He, too, would like protection for entry to Catholic schools without damaging the balance. As the school's image strengthens, Mr Gavin believes it could easily be filled by pupils living within one and a half miles if no restrictions are in place.
Catholic schools in Glasgow such as Holyrood, Scotland's largest, Notre Dame, the only all-girls school, with a high Asian intake, and St Andrew's Secondary in the east end are experiencing similar difficulties, as are some primaries. In St Joseph's College Dumfries, more than 50 per cent of children are not from Catholic families. John Oates, field officer for the Catholic Education Commission and chairman of St Andrew's College, the only teacher education institution for Catholics, believes there should be some kind of priority for Catholic children if a school is oversubscribed.
South of the border, Catholic schools can determine the criteria for entry. Something similar would be appreciated by some Scottish interests. The Catholic lobby failed to persuade Michael Forsyth when Scottish Secretary to relax the placing request rules. Parental choice was sacrosanct, especially as Mr Forsyth supported parents who wanted a strong religious basis for their children's education.
Ian McDonald, depute director of education in Glasgow, says: "It would be helpful if a local authority could determine the maximum roll a school could take. It could take in health and safety issues and a balanced curriculum and we could publish the information."
Helen Liddell, former Labour education spokeswoman, told Catholic heads she was committed to amending the placing request legislation to help councils reserve a small number of places in overflowing schools for children whose parents move into the catchment area after the first-year intake. Such an amendment would please John Stodter, director of education in Aberdeen, another city facing the problem of overcrowded schools.
No party would rescind parental choice but Mrs Liddell said she was unhappy that Mr Forsyth's "Balfron" amendment, initiated after problems at Balfron High in his Stirling constituency, failed to go far enough. It allows schools, particularly in rural areas, to reserve a small number of places. The Government may therefore consider further amendments along the lines recommended by the Catholic Education Commission.
Teresa Gourlay does not favour a quota system for non-Catholics - "we are well past the ghetto days" - but does argue for Catholic schools to be allowed to define their catchments in different ways, perhaps with a two-tier system of inner and outer areas. Such a definition would help schools that serve large areas of the cities.