A report commissioned by the Local Government Association from consultants Coopers amp; Lybrand says appeals on admissions by dissatisfied parents are to blame for over-sized classes in more than half of affected schools. A lack of classroom space is also a significant problem.
Meanwhile, the Government has insisted that parental preference should be enhanced and that surplus places in "poor" schools should not be filled by keeping children out of more successful ones.
Graham Lane, the LGA's education committee chairman, says the figures show the Government has to decide on its priorities.
"It has to change the law on admissions and appeals - that means reducing parental choice. If it is not prepared to face that, it is not going to deliver the targets."
Or, he says, the Government could still support parental choice by accepting higher numbers of surplus places.
The Coopers amp; Lybrand report, based on a survey of 45 authorities, puts forward five solutions - including revising admission numbers, creating mixed-age classes and team teaching. All have implications for accommodation, parental choice, fund-ing, andor local management of schools.
The report suggests that increased mixed-age teaching will be an inevitable consequence of reducing class sizes - while warning of the opposition of some governors, headteachers and parents.
Some heads concede they could reduce class sizes to 30, but are reluctant to if it means losing additional classroom assistants and non-contact time for subject co-ordinators.
The commitment of heads is vital for the policy - to find local solutions and to "sell" them to parents and governors - as education authorities can no longer "direct" schools to take action, warns the report.
Consultations on the draft regulations and guidance on reducing class sizes close on June 12. Assuming the School Standards and Framework Bill receives Royal Assent in July, education authorities will have to submit their class size statement by October 16.