The commitment, a key Labour election pledge, is running well ahead in Scotland where the maximum class size is already 33. Ministers introduced regulations in April, forcing councils to adhere to a three-year timetable for cutting classes in P1-P3.
Directors of education have criticised the policy for investing large sums of money - pound;48.2 million over three years - in an initiative that may not yield significant educational advantage. The cut from 33 to 30 is unlikely to change classroom practice, they say.
Several also complain of extra administrative burdens. Authorities have employed extra teachers and created additional classes.
John Wilson, head of quality development in East Renfrewshire, one of the councils with most pressure on places, said lack of accommodation was a continuing difficulty.
"We have had real difficulties taking forward the spirit of the legislation," Mr Wilson said.
The commitment would be met by team teaching and moving groups around to give a ratio of one teacher to 30 pupils.
Councils can apply to the Scottish Office for exemptions but East Renfrewshire has so far declined the offer. It is still waiting for Government announcements on the second and third years of funding before it can press ahead with building work.
Christine Pollock, depute director of education in North Lanarkshire, said staffing standards had been revised in all schools. Eleven out of 133 primaries faced building problems.
South Ayrshire expects only one or two difficulties in schools where accommodation is under pressure, although the picture will only be clear when pupils go back. Christine Pryce, head of resource development, said it had been "quite difficult" to meet the target.
John McKeown, head of educational provision in East Dunbartonshire, said 10 schools would have been over the limit had extra teachers not been employed. Some team teaching and additional classes would help fulfil the commitment. The process had been "awkward".
Bruce Robertson, director in Highland, is "confident" the limit will be met. As a rural authority, primaries tend to be smaller.
Alex McKay, Fife's director of education, said the council had introduced limits of 30 in the first two years of primary 2 during the past session and "with one or two exceptions" all schools would have limits of 30 up to primary 3 by the start of the new term. Fife initiated the policy before ministers seized on it, Mr McKay said.
In West Dunbartonshire, 14 teachers have been taken on on three-year contracts to allow all schools to cut classes to 30 up to primary 3.
Edinburgh has already employed 28 teachers with a further 20 due to start next month. Changes to regulations came too late to prevent difficulties with placing requests this year, Colin Dalrymple, head of education support, said. Some schools have been unable to adapt classrooms in time, leaving the city with no choice but to apply for special exemptions in "a few" cases.
"Unfortunately, certain schools will now have to be capped because no adaptations can be made to the building and therefore where in the past a full class was 33, this will become 30. This measure will reduce parental choice in some of the more popular schools and especially in inner city schools," Mr Dalrymple said.
Meetings with the Scottish Office confirmed officials prefer smaller classes to team teaching. Edinburgh wants to spend nearly pound;700,000 in adapting classrooms to promote lower class sizes.
John Patton, president of the Educational Institute of Scotland and a Clackmannan primary head, welcomed any class size reductions as an important factor in raising standards.