There were 54,600 cases lodged in 2014-15, up 8% on the previous year, Department for Education data shows.
Parents were successful in 23% of those cases that went to a hearing.
The DfE said the proportion of appeals being heard was stable amid a rising demand for places and that the admissions system was working well.
Many areas of England, especially major towns and cities, are facing an intense squeeze on places - particularly at primary school level - mainly due to a rising birth rate.
A breakdown of the latest government statistics shows there were more appeals concerned with places at state primaries than state secondaries.
There were 32,160 appeals over infant and primary schools; about 22,440 related to secondaries.
Not all appeals end up being heard. The number taken to an appeals panel was 40,014, up from 36,967 in 2013-14.
More than 9,000 were decided in favour of parents, with the percentage of successes staying almost the same as the previous year.
The data covers both local council-run schools and academies, which are not under local authority oversight.
A DfE spokesman said: "The fact that the proportion of appeals heard and upheld remains stable in the face of rising demand for school places shows the admissions system is working well."
All parents have the right to appeal if a school they applied to refuses their child a place.
The current system allows parents to argue that schools broke official admissions rules or that there are "compelling" extra reasons why their son or daughter deserves a place.
Figures published earlier this year showed that fewer youngsters got their first choice of secondary school this year, with around one in six missing out.
Overall, 84.2% of 11-year-olds got their top preference, according to DfE figures, meaning that around 15.8% did not. Last year, 85.2% got their first pick.
The figures also showed that 87.8% of children were offered their first choice of primary school, compared to 87.7% in 2014.
Rising numbers of parents in England are lodging appeals over children not being offered a place at a chosen school, figures show.