The growing pressure on Jewish secondary school places in London this year has led to calls for changes in the admissions system.

Gilead Limor, the founder of a support group for parents of children without a place, predicted this week: "The problem is not going to go away. It's only going to get worse."

As Jewish secondary schools report longer waiting lists, Jewish primary school headteachers have also expressed concern.

Angela Gartland, head of Rosh Pinah Primary in Edgware, where six pupils are still waiting for a Jewish secondary school place, said that this "continues to be a worrying time for parents. I feel strongly that a resolution needs to be found as I have anxious children who feel let down by the system. With pupil numbers increasing in the primary sector, this poses an increasing problem".

Eight pupils at Moriah Jewish primary, in Pinner, remain in a similar predicament. Headteacher Ruth Gafson said that parents were "feeling quite desperate. It is very stressful. By October last year, every child who wanted a place had got one".

Mr Limor, whose own daughter is one of those waiting, estimated that there could be 70 or more Jewish children in the same situation. He appealed for parents whose children had been offered a place at a school but were not planning to accept it to inform the school to free it for other families.

"My reckoning is that there are quite a number of spaces currently being occupied by children who are not going to take them," he said.

The number of children without any place at all was difficult to calculate because schools did not compare waiting lists, he explained, while some parents with a place at one school preferred their child to go to another.

"Take the example of a parent whose child has a place at JFS but wants them to go JCoSS as their first choice, and another parent in exactly the opposite situation," he said. "But there is no mechanism for them to switch.

"In addition, parents who have been offered more than one place should be obligated to make a choice within a specific time frame ."

Mr Limor said better communication between Jewish schools and between local councils could help to notify parents more quickly when vacancies occur.

Both JFS and Yavneh College have heard around 50 appeals each this year from applicants still hoping to get in. Yavneh's waiting list of 100 was "much higher than previous years at this stage", said its chairman, Susan Nyman.

A record number of siblings, 181, have taken many of the 300 places available at JFS. The school's headteacher, Jonathan Miller, said: "We share the frustration of parents who are yet to secure a place at a Jewish school for their child. We do still expect a small number of places to become available."

The waiting list at the cross-communal JCoSS was "significantly higher", said headteacher Patrick Moriarty. "There are several dozen on our waiting list but the situation remains dynamic. We would expect to make a few more offers."

Hasmonean High School, which caters for pupils from more Orthodox families, has extended places from 150 to 170, but it too has a waiting list.

But the request from Mr Limor's group for some schools to add bulge classes this year was not feasible, Mr Moriarty said. "It would create an unsustainable situation in future. We simply don't have the space to put more classes in. It's a physical non-starter."

Meanwhile, the education agency Partnerships for Jewish Schools is trying to find out exactly how many children are without a place. Chief executive Rabbi David Meyer said it would also be conducting research early on projected demand over the next few years.

The opening of new Jewish primary schools whose children are yet to graduate could add to the pressure down the line. There could be more competition in three years because some primaries opened bulge classes in that year group.