Teachers in 100 primary schools who responded to the survey are regularly taking classes of more than 35 children.
Slightly more than half of the schools which admitted that their biggest classes contained at least 35 children were in the North - 53 per cent compared to 47 per cent of primaries in the South.
Average-sized classes of 35-plus children were found only in schools in Liverpool, Nottingham, Barnsley, Bolton, Blackpool, Northumberland, Sheffield and Birmingham.
At Elsecar primary in Barnsley, average classes - taught by one member of staff - are 35. With the largest now comprising 44 children, Dave Pannett, the head, is having to teach full time.
He is working alongside Jan Hopwood, his deputy, teaching Year 6 pupils: "Otherwise she would have been on her own, and one person taking a class that big is just diabolical."
The 170-pupil primary issued a redundancy notice at the end of the summer term to a teacher to try to balance the books. It now has only five teachers and the head.
More headteachers are having to undertake either full-time or part-time teaching in an attempt to balance the books. That means paperwork and support for other staff often goes by the board.
Gerard Maloney, head of St Gregory's primary in Farnworth, Bolton, already teaches, but faced with the prospect of a 49-pupil reception class with just one teacher was considering taking that on as well.
In the end he was saved by a colleague moving to another job, which enabled him to recruit a cheaper newly qualified teacher.
Five primaries told The TES that their largest classes had 40 or more children; the schools were in Manchester, Merseyside, Barnsley, Bolton and Chippenham.A further 95 primaries said that their biggest class contained at least 35 children.
Overall, 44 per cent of 420 primary schools reported average classes of 30 or more pupils.
According to the Government, the average size primary class taught by one teacher this year is 27.3.
However, according to 420 primary headteachers responding to The TES survey, it is now 28.27. The picture was a little better in middle schools - 27. 6.
In secondary schools, where the Government has claimed that the average class is 21.6, headteachers reported an average class size of 23.6. Gillian Shephard, the Education and Employment Secretary, has consistently argued there was no evidence to prove that larger class sizes meant lower standards.
Her claims have been backed up by the Office for Standards in Education, which has said that class size was linked to pupil achievement only in the first two years of primary education.
But research commissioned by the National Association of Head Teachers has now challenged the Government's claims.
Christopher Day of Nottingham University said pupils in small classes misbehaved less, participated more, spent longer on their work and interrupted less often.