The New Israel Fund will oppose the nation-state bill "in any form which seeks to alter the vision of Israel's founders and harm Israel's democratic character," said the chief executive of its UK branch, Adam Ognall.
The Office of the Chief Rabbi and the Jewish Leadership Council have declined to express a view on the bill.
But Mr Ognall argued that British Jewry should be at the "forefront of the debate. The bill, in its various forms, has the potential to fundamentally alter Israel's dual essence as a Jewish homeland and a democracy." It also had "the potential to impact Israel's relationship with Jewish communities and its supporters."
Earlier this year, the JLC hosted a seminar on the proposed law given by the Jerusalem-based Jewish People Policy Institute. The JPPI, which was asked to undertake the consultation by Justice Minister Tzipi Livni, has warned that the bill could have adverse consequences.