With 704 applications for just 90 places this September, even a vicar's daughter was unable to get into Lady Margaret school, a Church of England secondary in west London.
The school heard 97 appeals last week, at a total cost of almost pound;7,000. Just three were successful.
Joan Olivier, the headteacher, believes the pan-London admissions system, which was supposed to iron out deficiencies in the process, has made it worse.
Previously parents wanting a single-sex, church education for their daughter could have applied to three suitable schools in that part of the capital, the other two being the Grey Coat Hospital in Westminster and St Marylebone in Camden, and probably got into one of them.
Now, they have to list preferences, and failure to get into the first choice leaves no chance of getting into the others.
Mrs Olivier said: "I raised this with ministers and Professor Tim Brighouse, the London schools commissioner, but they said I was being alarmist.
"It is an absolute nightmare. We had to use couriers to transport 23,000 bits of paper across London to the appeals panels, and two additional admin staff were employed to make sure the paperwork was completed in time.
"I spent four nine-hour days listening to appeals, knowing there was little or no chance of them being successful.
"The cost is huge, not just in time and effort but in real monetary terms.
Photocopying alone came to more than pound;1,100.
"Most parents were wonderful and I was sorry we could not help them. But some were hostile and aggressive. At one point one of the panel had to leave the room and have a coffee to calm down.
"Amazingly, we had to turn away a vicar's daughter. She scored highly on church attendance and religious knowledge but badly on proximity. That is how ridiculous it has become."