The controversial knife-edge decision to introduce school catchment areas into Brighton and Hove could be reviewed.
Eight Conservative members of the city's council have labelled the vote used to bring in the measures "flawed".
Councillor Vanessa Brown, the Conservative education spokeswoman, said: "Too many parents are angry at the way in which the committee's decision was taken. In particular, they believe the last-minute sacking of Juliet McCaffery did not constitute open politics' or a fair conclusion to debate."
The group have written to council chief executive Alan McCarthy, asking for him to "call-in" the issue because they believe it has broken parts of the council constitution. If he agrees, a scrutiny committee would have to be convened within seven days to decide whether it would be necessary to send the matter back to the children, families and schools committee, which made the vote last Friday.
That committee would then have to rule whether to push the plans through, make changes, delay them or scrap them.
The new system was voted in after Labour rebel Juliet McCaffery was thrown off the committee by her party for refusing to vote for the plans. As a result, the poll was tied five to five and committee chairwoman Pat Hawkes used her casting vote to approve them.
In their letter to Mr McCarthy, councillors Vanessa Brown, Linda Hyde, Dee Simson, Brian Oxley, Ted Kemble, Ann Norman, Ken Norman and Mary Mears said:
Some parents had been unaware of the implications of the catchment area plan despite the council consultation.
- Information provided to parents who helped make the proposals had been incomplete, conflicting and sometimes late.
- If Coun McCaffery had to be removed from the committee it should have been done when she first expressed opposition months before the vote.
- Parents had been misled into believing Coun McCaffery would have a vote to cast and had taken time to lobby her.
Conservative group leader Brian Oxley said: "This sort of politics is exactly what makes people lose trust in politicians and puts them off voting."
Hundreds of parents celebrated the introduction of the catchments, which was intended to address failures of the existing walking distance-based system.
Children in parts of east Brighton, the seafront and central Hove have been too far from their nearest schools to gain priority places.
Hundreds more parents are furious the new catchments have cut them off from their nearest school.
One group of prospective parents for Longhill School in Rottingdean met last night to consider opposing the new system.
To see a map of the new catchement areas, click here