A thorough investigation was today launched into where to teach up to 40 Basildon children.
Parents were warned by education bosses their children may not get a place at the school of their choice even if they live within the catchment area.
The message came after 100 parents applied for just 60 places at the top-ranking Great Berry County Primary School in Laindon.
With many surrounding schools already full, education chiefs said they were considering their options, but indicated parents may have to settle for second best.
Great Berry was the district's second most successful school in this year's government league table.
An increase in the number of homes built in Laindon over the last two years has added to the pressure on Great Berry and surrounding schools.
More than 430 pupils are currently being taught at the school - ten over its capacity - while Lincewood and Merrylands are also full up.
There are still places available at Bluehouse and Millhouse. Nearly 30 children refused places at Great Berry live inside the school's catchment area.
An Essex County Council education spokesman said he appreciated parents' concerns.
He said: "We have begun a thorough investigation into the problem of places at Great Berry and will try to find a number of options.
"We are well aware of the concern from local residents about the shortage of places for their children.
"For the last two years we have not been able to guarantee a place at the school for children in the catchment area because of the number of families who live there."
Parents are set to call a meeting with education chiefs to discuss the problem.
Councillor Bob Sears, Labour member for Langdon Hills, said he had been overwhelmed by calls from angry parents.
He said: "The problem has arisen because when the school was built the majority of homes in the area were not here, so the school was filled up with children from outside the catchment area.
"We need to extend the school - there's plenty of room there. My advice to parents is to make sure they get a good appeal in."
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