The secondary schools in the most popular of Brighton and Hove's new catchment areas will not be able to handle all of the pupils in their expected intake, their heads have said.
A late amendment to new school admissions proposals given the go-ahead on Friday stated that extra places would be provided if there were more children in any catchment than spaces at the relevent schools.
But yesterday headteachers Trevor Allen and Andy Schofield, from Dorothy Stringer and Varndean schools, said they would be unable to accommodate the number of pupils likely to be involved.
Mr Allen said: "We have been taking additional pupils for the past four years and are already stretched further than we should be.
"There will come a point where it would be detrimental to the students. It means bigger classes which creates more problems, especially in specialist spaces (like computer rooms) which are only equipped to take a certain number."
The two schools have been allocated a catchment which is expected to be heavily oversubscribed.
Original council calculation missed out a group of 66 children in the area and it was later revealed the schools could be obliged to take on 74 pupils who live outside the catchment but have siblings already attending.
The council has repeatedly assured parents it will make extra provision to make sure the catchments work.
Mr Schofield said: "We have had tentative approaches from the council to see if we could take on more pupils. We are willing to work with them but there is a limit to what we can do.
"We will need investment in the infrastructure, we are at capacity at the moment so building work will be needed. There's no way we will have it forced on us on the cheap."
Mr Allen said he had never been asked about taking on more pupils. He has been openly opposed to the controversial catchment areas which have cut his school off from several primary schools which have acted as feeders.
He said: "I would be disinclined to accept the outcomes of what I think to be a disturbing set of proceedings."
Mr Allen said he was appalled that city councillor Juliet McCaffery had been removed from the council schools committee at the last minute.
Many parents in Patcham, Westdene, Withdean and Prestonville have been angry they have been excluded from Dorothy Stringer's catchment.
Their frustration will be increased by the announcement yesterday that the school has been rated "good" by Ofsted inspectors, who described some features as outstanding.
Mr Allen said: "They've said some very nice things about us and we're delighted by it."
- To see a map of the new catchment areas, click here.