In the playground of Ilford Jewish Primary School, Chinese pupils race with boys in kippot. At King David in Birmingham, the Ivrit prize in assembly could go to Shimon or Shabina.

For the schools which must accept non-Jewish pupils, the atmosphere is harmonious, albeit after considerable challenges. But it is a challenge which north-west London schools could yet face.

On the face of it, Jewish schools have never been more popular. The last major survey by the Jewish Leadership Council in 2008, and a follow-up in autumn 2011, shows that there are now more than 26,000 Jewish pupils attending Jewish schools compared with under 13,000 30 years ago. Around 30 per cent of that increase is from the mainstream community. Around 60 per cent of Jewish schoolchildren entered Jewish schools in 2011.

But the JLC said: "The major cloud on this sunny horizon is numbers." With the opening of JCoSS and Yavneh College, and the expansion of JFS, around 1,000 Year 7 places are now available, a 50 per cent increase.

Two other major changes could have an effect on school places in the coming years. The Supreme Court ruling in the JFS admissions case has meant that pupils must complete a certificate of religious practice, and the new free schools can only accept 50 per cent of pupils on the basis of religion.

The vital thing is that every child who wants a Jewish education can have one

Two new free schools, Etz Chaim and Eden Primary, have now opened in north London. The JLC figures show that, in less than ten years, unless births or migration increase, every Jewish child in the country would have to go to Jewish schools if the schools were to be filled exclusively with Jewish children.

Lira Winston, co-ordinator of the JLC's schools strategy implementation, said: "It's a really difficult one. We don't want to discourage people setting up Jewish free schools. But parents should consider it very carefully, making sure they have done rigorous research into the numbers."

Where supply of Jewish places outstrips demand in state-funded schools, government policy is that schools must accept non-Jewish pupils.

Spencer Lewis, head of King Solomon High School in Redbridge, whose non-Jewish intake this year was 40 per cent, warns about the recent surge in Jewish school building.

"I am concerned at the ease with which free schools can now be set up. There seem to be more school places than Jewish children to fill them. In the future it will not only be King Solomon High School with students from other faiths, but many other schools as the community continues to overstretch itself and its resources."

But Mr Lewis stressed that KS Jewish education was still traditional. "This has of course been a challenge in ensuring that the Orthodox ethos of the school is maintained, while ensuring that all students feel at home in the school. All boys at King Solomon wear kippot, everyone participates in the celebration of chagim, everyone learns Ivrit and Jewish studies."

Like King David Primary in Birmingham, where more than half of the pupils are Muslim, Mr Lewis has observed many of his non-Jewish pupils come from religious homes. "Those of other faiths choose KS because they value the things that we value: the importance of community, charity and the value of hard work."

One-third of the pupils at the local Ilford Jewish Primary are also not Jewish, although the school predicts numbers will rise in coming years. Headteacher Roz Levin and Mr Lewis, who will soon share a campus in Redbridge when IJPS moves to the KS site, agree that the issue could soon arise for schools in north west London.

In the middle, metaphorically and geographically, is Hackney's Simon Marks Primary, where 10 to 15 per cent of the pupils are not Jewish. Headteacher Gill Ross said: "We have secular families, Israelis and Charedi pupils, from a mix of socio-economic backgrounds. We teach the children a high standard of Hebrew and Jewish education, and the diversity is celebrated."

Neither the north east London nor Redbridge schools, including primary Clore Shalom, face anything like the same challenges as King David in Birmingham, which in 2010 had only 65 Jewish children out of a roll of 245, or King David High School in Liverpool where Jewish students account for just under 15 per cent of its 660 pupils.

In Manchester, King David High School is booming, says chair of governors Joshua Rowe, but that has not always been the case. His school is proof that a community can turn around a decline in Jewish education. "Until 1993 King David was a failing school, threatened with closure, that's how I got involved. We were losing half our community. Nobody was lifting a finger to help a school threatened with closure. King David had 200 kids in 1990, now we have 850."

Getting top results was the only way to bring parents back, he said. But now pupil numbers have halved in the infant school, which he said was the school's failure in the early 1990s "coming home to roost. The hope is we can reverse the trend through our success in the senior school; hopefully they will marry someone Jewish and stay in Manchester. In the nursery and the crèche, we have about 120 kids, so perhaps we are seeing the beginning of growth."

He warned against the proposal for a Jewish free school in Leeds. "It's a big mistake. It will end up like Birmingham and Liverpool. I want KDHS to be a hub school for the North West. Leeds and Liverpool kids should come here."

In the densest Jewish areas, most Jewish schools are, for now, full to bursting. Co-chair of the Association of Headteachers of Jewish Schools, Vivienne Orloff recently retired as head of Europe's largest Jewish primary, the modern Orthodox Michael Sobell Sinai in Kenton. "Success breeds success. We have over 680 children, out of our 90 children in Year 6, now virtually every child continues their Jewish education into secondary."

She too, is concerned that more schools could mean more empty places. The school, normally over-subscribed, was asked to take one non-Jewish child in September. "New schools can be a waste of resources; people need to be more creative about what's available. But the most important thing is that every child that wants a Jewish education can have one."

JFS is still the largest Jewish secondary school in Europe. Head Jonathan Miller said: "More and more parents are convinced of the value of Jewish schools, the excellence of the academic results, the importance of the Jewish journey pupils go on, I don't buy the wishy-washy argument that Jewish schools don't equip you well enough for a multicultural society, In terms of facilities we have the same as the top independent schools – and you don't have to pay for it."

The head of the country's newest Jewish secondary school, Jeremy Stowe-Linder, believes competition, particularly the arrival of his cross-communal JCoSS, has been good for the continued excellence of Jewish education.

"I have a marketplace take on it. Build it and they will come. We are, as a community, slowly coming of age."