The Chief Rabbi, Lord Sacks, will back a unilateral move by Orthodox groups to reverse the JFS court ruling if it proves impossible to achieve broader communal agreement.
However, his office stressed in a statement that he still believed the Board of Deputies to be the "most appropriate body" to pursue a change in the law.
Jewish schools were forced to introduce new entry rules last year after the Supreme Court upheld an Appeal Court decision that schools could no longer choose pupils on the basis of whether their mother - or father - was Jewish.
Lord Sacks's office said that he remained in close contact with the Board of Deputies, which was seeking "consensus on the way forward".
But it added that he was also in touch with "those Orthodox institutions which are considering making a separate approach to achieving legislative change".
While the Chief Rabbi thought legislative change "desirable", it should be sought "only after the fullest consideration of how this can best be achieved", his office stated.
"The Chief Rabbi remains hopeful that an accommodation can be reached which would enable the community to move forward on this matter with all sections united - but will fully support a separate approach by the Orthodox bodies, including the United Synagogue, if wider consensus cannot be achieved."
Three months ago, Conservative schools spokesman Michael Gove told the Board of Deputies that it was important for the Jewish community to speak with a "united voice" for legal change.
But the Board of Deputies was unable to secure a community-wide agreement before the general election.
The Reform and Masorti movements have previously indicated they would only back an amendment to the law in return for an understanding from the United Synagogue that it would accept the children of non-Orthodox converts into its schools.
Meanwhile, the Liberals so far appear reluctant to countenance any rewriting of the statute books. At the movement's biennial conference only last month, its chief executive Rabbi Danny Rich criticised "special pleading" by religious groups in Britain, including what he said were attempts by the governing bodies of Jewish schools to "seek exemption from the Race Relations Act".
Since Jews are legally defined as an ethnic, as well as a religious, group, the courts ruled that to make school entry conditional on parental descent was a matter of ethnic origin - and therefore racial discrimination.
In the past few months, Sephardi leader Rabbi Abraham Levy, one of the Board of Deputies' two ecclesiastical authorities along with the Chief Rabbi, has been holding talks with representatives of other Jewish streams over what to do about the court ruling. "All I am trying to do is to see whether we can find some common formula which will make most of Anglo-Jewry happy," he said.
But also active has been Rabbi Jonathan Guttentag, of the National Association of Orthodox Schools, who recently convened a meeting of Orthodox groups. It was an effort to "bat ideas around the table" prior to a requested meeting with the Chief Rabbi, he explained.
"Realistically, the Chief Rabbi holds the key," he said. "No government minister can take any representation seriously without the Chief Rabbi."