The race to open a new Jewish secondary in the London area has intensified, with a third group announcing plans to open a free school.

The Hertfordshire Jewish Free School (HJFS) hopes to apply to set up a new Jewish school in the county in September, while Kedem High and Barkai College are aiming to do likewise in Barnet.

But it is possible that one or more of the groups might combine their bids as they seek to solve the acute shortage of Jewish secondary school places predicted in north-west London over the next few years.

Maurice Ashkenazi-Bakes, one of the backers of HJFS, said that his group had had a "positive" meeting with Kedem and was "open to dialogue" with Barkai. "We'll decide whether to work with another group or to go ahead on our own."

But he said he believed that the "incredible" growth of the Jewish population in Hertfordshire fuelled the need for a new Jewish secondary school there, in addition to Yavneh College.

Chief Rabbi Ephraim Mirvis, however, has made clear his reservations about a free school. He argued that since it could only reserve half its places to Jewish children, it would leave open the possibility of having to take a large number of children from other faiths.

A spokesman for his office said that the value of Jewish schools lay in providing "a completely immersive Jewish environment - something which is far more challenging if the 50 per cent rule associated with free schools is applied."

He added that "as such, our focus must be on the options which meet the need for secondary education places, avoid the challenges posed by the current free school model and deliver for our community a centre for excellence in both religious and secular terms".

The educational agency Partnerships for Jewish Schools forecasts a shortall of 90 places a year over the next five years, adding that the demand could be higher. Its figures exclude an extra 44 places offered this year by two schools, Hasmonean High and Yavneh.

Mr Ashkenazi-Bakes, who lives in Bushey and has three children at Hertsmere Jewish Primary School, argues that there is also a significant number of parents in Hertfordshire who do not bother to apply for their children to go to Yavneh because they live outside its main catchment area but who would be attracted to another local Jewish school.

The United Synagogue is understood to be exploring the option of relocating Kantor King Solomon High School, which has a minority Jewish intake, from Essex to north London.

But David Collins, director of young people and young families in the US, has warned that "multiple competing proposals for new schools, if all were implemented, may lead to serious problems, therefore we are keen that a co-ordinated approach is adopted."

He added that "working with Pajes, we are confident that we are able to create the school places needed in areas where the requirement is growing over the coming years in a measured and strategic way".

One option remains to increase the intake of existing Jewish schools beyond their current maximums, rather than have a new school.

Some Jewish schools are known to be concerned about the potential impact on their numbers if a new secondary school opens, but have refrained from making their anxieties public.

As for expanding, Yavneh has insisted that its bulge class of an extra 30 children this September is a one-off.

Hasmonean plans to accept 194 children - 14 more than its original limit of 180 this year.

Patrick Moriarty, the headteacher of the cross-communal JCoSS in Barnet, said that the school could not take a bulge class. "We don't have the space," he added. "The only way we could take more people is if there were a permanent expansion and we had external capital funding for it."

As for moving King Solomon, its headteacher Matthew Slater emphasised that "our entire focus is on the provision of outstanding education for the Jewish population of northeast London and Essex".

Providing extra places for north-west London required "further discussion".

Andrew Rotenberg, the instigator of Kedem, said his group had had a "very constructive early meeting" with the HJFS group. "I was very encouraged," he added. "I see there is room to work with that group in the common interest."

Barkai's Eve Sacks said that her group spoke "regularly" with HJFS but that it was "hard to do a joint project due to geography".

While Barkai favoured a London location, "if the Department for Education can only find us a Herts site, then who knows?"

Robert Leach, headteacher of Michael Sobell Sinai Primary School in London, pointed out that one of its pupils failed to find a place at any local Jewish secondary school last year.

The admissions system was "traumatic for the parents and for the children", he said.

Mr Leach felt that more could have been done by existing secondary schools.

"Some could have opened up bulge classes instead of having to explore new options."