Parents living near Tretherras School in Newquay are angry their children have been denied a place.
Cornwall County Council has confirmed the school did not follow clear procedures and protocols.
The school has refused to comment, but a council spokeswoman said the school's board of governors took the matter very seriously and a thorough investigation was carried out by auditors after a complaint from a parent.
A statement said: "Our investigation showed our clear procedures and protocols were not followed by the school in this case.
"The school has co-operated fully in the investigation and has given a complete assurance that it will fully comply with the admissions procedures in the future."
It said current legislation forbids it from removing the pupil from the school.
Local MP Dan Rogerson said: "Clearly every school has a responsibility to abide by its own admissions policy.
"I hope a conclusion can be arrived at which protects the interests of all the children involved."
