The Board of Deputies has distanced itself from threatened legal action by a Sikh group to have both communities included as ethnic groups on the next census.
Both Jews and Sikhs are recognised for the voluntary religious question, which was introduced at the last census in 2001.
But whereas both are legally classified as ethnic groups - unlike Hindus or Muslims, recognised only as religious communities - they are not listed in the ethnic category on the census.
The Sikh Federation UK, a radical organisation which supports the creation of an independent Sikh state in the Punjab, said it would mount a legal challenge against the Office of National Statistics for Sikhs to be identified as ethnic on the next census.
SFUK wants the census to "reflect both the religious and racial identity of both Jews and Sikhs", Gurjeet Singh, its national press secretary, said.
It also accused the ONS of "working behind the scenes to undermine" the proposed change by "exerting pressure on the Board of Deputies".
But Daniel Vulkan, the Board's research and information officer, rejected any suggestion of being under "any kind of pressure or undue influence".
He explained: "In our formal submission to the ONS, we requested that 'Jewish' be included as one of the options under the ethnicity question. However, we understand the reasons why this did not prove to be possible."
He added: "It would also seriously compromise the ability to compare the results of the 2011 census with those from 2001. This comparison will, for the first time ever, provide invaluable information relating to changes in the size and profile of the Jewish community over a period of time."