Appeals against places allocated for primary schools have jumped from 33,000 to 38,000 - a rise of 16.8%.
At secondary level, there was a drop in appeals - down from 53,400 to 50,200.
The government says the figures show an increasing number of parents are unhappy with the school choices which are available.
Appeals have risen dramatically in the past few years - almost doubling since 2004.
A rise in the number of school-age children has increased pressure on school places, particularly in hot spots such as London and Birmingham.
When parents appeal against a school place allocated to their child, their case can go on to be heard by an independent panel, which decides whether the decision was fairly reached.
The panel assesses whether the school or admissions body (often the local council) followed its procedures correctly.   Parents can also argue that there are "compelling" extra reasons why their child should go to that school.
If the parent succeeds, their child is usually given a place there.
Schools Minister Nick Gibb said: "The figures show that an increasing number of parents are unhappy with the school choices open to them.
"The level of dissatisfaction underlines why it is so important we change the schools system so providers like teacher groups and charities can open new state schools wherever parents want them; and give outstanding schools the freedoms they need to help improve those in more challenging circumstances."
Statistics released on Thursday relate to appeals lodged in 2008-09.
They show that while appeals against primary places rose, parents were less likely to be successful in them than in the previous year and secure a place for their child at their chosen school.
One quarter of parents whose primary school cases were heard by an appeals panel were successful  - down from 27.8% in the previous year.
The chances of success were higher at secondary level, with 33% of parents winning their case, up slightly on last year.
Rates of appeal vary across England.  The highest rates for primary school appeals are seen in Bradford and Leeds, Birmingham and in parts of London.
At secondary level, parents in London are the most likely to appeal.
The number of parents appealing against their children's primary school places in England has risen again, government figures show.