The number of classes for five to seven-year-olds with more than 30 children rose from 65 last year to 530.
Schools and local authorities have been legally obliged since 2001 to ensure that five to seven-year-old pupils are taught in classes of 30 or fewer.
But the Government's figures, based on a census of schools in January, found 740 classes were over-sized.
Of these, 210 were considered exempt because they had pupils admitted on the basis of their special needs, an appeals panel decision, or outside the normal admissions round.
Around 50 of the classes contained more than 36 pupils, the first time that such large groups had been recorded in more than five years.
Teaching unions said the increase in large infant classes was related to a drop in the numbers of five to seven-year-olds in primary schools. The total fell by more than 21,000 last year to 1,430,700.
A spokeswoman for the National Union of Teachers said: "The numbers of pupils in year groups don't drop in neat packets of 30. Schools with 31 or 32 pupils in a class are in a difficult situation because they have to decide whether they are going to employ an extra teacher and create two classes of 16.
"It's a terrible dilemma, especially if you are a small primary with a one-form entry, though schools must do their utmost to abide by the law."
David Hart, general secretary of the National Association of Head Teachers, said the fall in pupil numbers meant schools had less money for teachers and less flexibility with staffing. Mr Hart said that the introduction of guaranteed non-contact time in September, to allow teachers to plan and prepare lessons, would make it even harder for schools to keep class sizes down.
The figures were seized upon by the Conservatives, who said they showed that the Labour government had broken its pledge to reduce class sizes.
Other statistics in the report were, however, more positive.
The average size of infant classes fell slightly this year to 25.6 pupils.
And the proportion of primary pupils in classes of 31 or more has dropped from 21 per cent to 15 per cent since 2001.
A separate report showed that the number of teachers has risen by 32,500 since 1997 to 431,700, The report, Pupil Characteristics and Class Sizes January 2005, is available online at www.dfes.gov.uk