School leaders are calling on politicians to end what they call "the misleading rhetoric" of school choice - which, they say, cannot be delivered.
Schools say admissions appeals consume hours of their time
The challenge has been issued by the Association of School and College Leaders (ASCL) and Foundation and Aided Schools National Association (FASNA).
ASCL leader John Dunford said those who did not get in to the more desirable schools in England felt hard done by.
Letters about secondary school allocation are being sent out later.
Meanwhile, a parental advice charity has begun a text message service on how to appeal.
The admissions regulator, chief schools adjudicator Philip Hunter, has said that the present system of admissions and "parental choice" is fuelling social and racial divisions.
He has said that options that will be unpopular with many parents, such as having local lotteries for places, might be necessary.
ASCL general secretary John Dunford said: "Because there will always be schools that are seen by parents to be more desirable than others, there will always be parents who do not get their first choice and feel hard done by the system.
"It does not necessarily mean that the second and third choices are poor schools," he said.
"Parents have been led to believe by political rhetoric from all parties that they have a right to send their child to the schools of their choice.
"When parents are disappointed, they turn to the appeals system which then leads to huge amounts of bureaucracy for schools."
The most popular, oversubscribed schools then spent many hours which should be used for teaching and learning, justifying admissions decisions.
The FASNA's general secretary, George Phipson, said most schools had very straightforward criteria for deciding who got in.
"It is unhelpful for politicians to appear to suggest that by expressing a preference for a school parents are able to circumvent the result of such criteria from being fairly applied at oversubscribed schools," he said.
There were more appeals - and increasingly lawyers were being used, he said.
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The result was that many hours were spent in appeals which simply confirmed the original decision.
Instead the two organisations urge the adoption of an additional stage in which an appeal was first scrutinised by an independent panel to determine whether the grounds were valid.
Meanwhile, the Advisory Centre for Education is launching a free, independent advice service, delivered via text.
It will be available from Tuesday when families start receiving their allocation letters.
Advice can also be accessed via the ACE's website.
The government says its answer to the problem is to make all schools good schools.
On Friday, the adjudicator, Dr Hunter, suggested that among other things lotteries might be used to spread applications more fairly across schools.
In Brighton, East Sussex, for example, a tie-break system was introduced last year - to the consternation of some parents.
The local council says its geographical spread of schools meant people in some areas had a realistic chance of receiving offers for all three of their secondary school preferences. In others they had no chance.
Under the new system, all applicants are allocated a randomly-generated number for each of the schools they list as a preference.
If there are more applicants for a school than places, they are ranked on the numbers they hold. Places are allocated in that order.
"The vast majority of those who did not get a place at that school will get a place at one of their other preferred schools," the council says.