East Renfrewshire describes the situation as "acute in both the primary and secondary sectors". The tiny authority faces a Pounds 9 million bill to build extensions at five schools as a matter of urgency but can only find Pounds 3.4 million.
East Dunbartonshire reports that 63 per cent of requests are from outwith the authority. Michael McCarron, the council's education convener, wants to meet Malcolm Green, his Glasgow counterpart.
Of 1,150 requests this session, 731 were from outside East Dunbartonshire and 15 per cent were refused "mainly due to pressure on accommodation", the council's education committee was told.
Officials estimate that 37 per cent of requests for secondary schools are a direct result of parents affected by Glasgow's closures programme. The schools most affected are Bearsden and Boclair academies, which are a magnet for Drumchapel parents, and Bishopbriggs, Turnbull and Thomas Muir high schools, which attract pupils from the Milton and Springburn areas of Glasgow.
Pressure on accommodation has forced East Renfrewshire to deny some local pupils a place at three of its 24 primaries, Netherlee, Kirkhill and Busby.
The primary 1 intake at the 658-pupil Netherlee has swollen by 60 per cent because of families moving into the area, with the result that a permanent extension planned to meet a roll of 826 by 2004 is already too small.
The authority has plans for a Pounds 10 million privately funded package to rescue two schools, replacing Mearns primary and extending St Ninian's High. By 2001, the primary will be 72 per cent over capacity and St Ninian's will have 58 per cent pupils too many.
The problems of full primaries have impacted on secondaries such as Williamwood where the accommodation crisis is described as "critical", and Mearns Castle where three feeder primaries have rising rolls.
The council's education committee agreed on Tuesday to press for a meeting with Scottish Office officials. Although there is cash to reduce class sizes and improve school buildings, the Government has made clear that there is no ministerial enthusiasm for limiting intakes to popular schools at the expense of parental choice.