The proportion of primary pupils in illegally large classes more than doubled in the past three years, government figures show.
Labour promised to cut class sizes, outlawing the practice of teaching children aged seven and under in groups of more than 30.
But since January 2002, the first year the law came into effect, the proportion of pupils in England in classes of more than 30 jumped from 0.6 per cent to 1.6 per cent by January this year.
The statistics reveal 22,080 infants were in illegally sized classes in January 2005, representing a 6.5 per cent rise in just 12 months. Officials said the majority of large classes would have broken the legal limit for one of several "permitted exceptions", such as pupils joining schools late.
But Mick Brookes, general secretary of the National Association of Head Teachers, said schools were being forced to increase class sizes to deliver planning preparation and assessment time for teachers, which became a statutory requirement in September.
"The fact that classes are rising doesn't surprise us at all," he said. "We are pretty certain that one of the ways PPA time is being covered is by increasing class sizes."
The figures show that average class sizes for infants fell slightly to 25.6. But the average junior class size went up from 27.2 pupils last year to 27.3 in 2005.
This year, 15.2 per cent of all primary school pupils - aged 11 and under - were in classes of 31 or more, down from 21.1 per cent in 2001.
The Department for Education and Skills said: "We are talking about no more than an additional 40 classes out of 55,860."