The overwhelming majority in a survey of parents of Jewish pupils at Jewish schools say they would accept the admission of non-Jewish children.
Around half of the survey, conducted among parents of the three Jewish schools in Redbridge in Essex, would feel it acceptable for non-Jewish children to make up 10 per cent of the roll - while roughly a quarter of the parents would accept up to 25 per cent non-Jewish pupils.
But around a quarter of parents regarded it as "unacceptable" to admit non-Jewish children, according to the survey, commissioned by the Jewish Leadership Council's schools strategy implementation group.
The JLC has warned that rising numbers of Jewish school places could lead to non-Jewish children having to be admitted anyway in some parts of London - because there were not enough Jewish candidates to fill them.
This latest research has been carried out in Redbridge, because of the diminishing local Jewish population.
"Falling Jewish enrolments in the schools mean that places must be offered to non-Jews" in the area, the report says, posing practical questions over non-Jewish participation in Jewish observance and studies, and the cost of providing education in other faiths.
The two Orthodox schools in Redbridge - Ilford Jewish Primary School and King Solomon High School - have already taken in some non-Jewish pupils in 2009: five among 31 first-year pupils at IJPS ( although it hopes its Jewish intake rises to 55 this autumn), and seven among 122 at King Solomon.
An alternative to admitting non-Jewish pupils by reducing the size of the schools is "difficult", the report says, because King Solomon has already been refused permission to reduce its entry from five to four forms: Ilford has dropped from two to one and a half this year.
The JLC already supports a plan to relocate Ilford Primary to the site of King Solomon.
But the report notes that the third Redbridge school, the pluralist Clore Tikva Primary - which is also a feeder school to King Solomon - fears that this arrangement could make co-operation with King Solomon more difficult.
Lenna Rosenberg, head of Clore Tikva, said this week that she would like her school "to become part of a larger Redbridge campus, including IJPS and King Solomon. It would require some education provision that would not compromise anyone's religious beliefs."
The survey found strong overall support for Jewish schooling among parents, although noting that fewer than 40 per cent make voluntary contributions for Jewish studies.