There is no evidence that children in smaller primary classes do better in maths or English, researchers say.
Teachers get stressed trying to meet individual needs - research
And factors such as teachers' age and level of experience have no influence on pupils' attainments in any subject.
A team at London University's Institute of Education studied thousands of pupils in their fourth, fifth and sixth years of schooling in England.
Pupils in larger classes made more progress in literacy in Year 6. Poorer children did less well throughout.
The study was set up because "despite the vigorous debate" on the subject, research to date had not given a clear picture.
A summary of the findings has been published on the Department for Education and Skills website.
It said statistical analysis pointed to "a clear conclusion": there was not found to be any evidence that the size of class had any impact on progress in maths or literacy in Year 4 or Year 5.
Nor was there any apparent effect on progress in maths or science in Year 6.
There was "a positive relationship" between class size and Year 6 literacy: pupils in larger classes made more progress.
"There was no evidence that any of the characteristics of teachers, such as their age, level of experience, length of time in the current school had any influence upon pupil attainment in any discipline," the report also said.
Pupils eligible for free school meals - an indicator of family poverty - began with lower scores and fell further behind. So did those with special educational needs.
Girls did better in literacy; boys in maths. Ethnic grouping was not found to influence children's progress.
The team identified complex relationships between class size and what they call classroom processes.
For example, larger classes tended to have more groups with more children in them - so some might "freewheel" and miss out on the teachers' attention.
Questionnaire responses showed teachers worried they could not meet the needs of all children in large classes.
Discipline in large classes could also be more difficult. Finding time for marking, planning and assessment was more of a problem.
Teachers used various "coping strategies", the report said.
"This attempt puts them under enormous strain, as the ideal outcome becomes more and more impossible to achieve."
The team suggested more could be done in teacher training to tackle this.
Alternatively, there could be more group work involving pupils learning together.
The Liberal Democrats have promised they would cut primary class sizes if elected to government to a maximum of 25 pupils within five years and, if re-elected, to 20.
Currently the only legal limit is of 30, for those in infant classes (school Years 1 and 2).
In Wales, the assembly government has invested in reducing primary classes to below 30 as well.
The effect of class size on attainment and classroom processes in English primary schools (Years 4 to 6) 2000-2003 by Peter Blatchford, Paul Bassett, Penelope Brown, Clare Martin and Anthony Russell, Institute of Education, University of London.