The attack, in a leaked letter to a right-wing Orthodox Jewish leader, intensifies the row between the Orthodox tradition and the Reformists over Dr Sacks and his attitude to Rabbi Gryn, a Reformist.
Last night, Rabbi Dr Jonathan Romain, spokesman for the Reform Synagogues of Great Britain, called on Dr Sacks to renounce his title. "Clearly, the Chief Rabbi no longer represents all Jews and speaks only for the Orthodox sector," he said.
"He no more represents Reform and liberal Jews than does the Archbishop of Canterbury represent Catholics and Methodists."
The acrimonious dispute followed Dr Sacks' non-attendance at the funeral of Rabbi Gryn, which angered the Reform movement, and his presence at a later memorial ceremony, which in turn caused outcry among some Orthodox Jews.
In his letter, leaked to the Jewish Chronicle, Dr Sacks said that his only reason for attending the memorial was to avoid giving the Reform movement a reason for appointing its own chief rabbi. He said Rabbi Gryn was one of "those who destroy the faith" as part of a "false grouping".
He assured Dayan Chanoch Padwa, the 90-year-old head of the Union of Orthodox Hebrew Congregations, that he was paying recognition to Rabbi Gryn, "not as a Reform rabbi but as a survivor of the Holocaust".
Supporters of Rabbi Gryn, who was known to millions through his appearances on BBC Radio 4's Moral Maze and Thought for the Day on the Today programme, said the letter could lead to large numbers of British Jews dissociating themselves from the Chief Rabbi.
Although Dr Sacks is technically the Chief Rabbi only of the United Synagogues, the main Orthodox group, he is seen by many Jews and non-Jews as the leader of British Jewry.
Dr Sacks described the leaking of his "Not for Publication" letter, which was written in Hebrew, as a "scandalous betrayal" and attempted a damage limitation exercise by writing an explanation of the context of the letter in the Jewish Chronicle.
He praised Rabbi Gryn as "a man of courage and deep humanity", but stopped short of retracting his attacks on his religious work.
Dr Sacks called on all Anglo-Jewish leaders to join in a Coalition for Peace in the Community to prevent disunity. "We must now call a halt to the debate over Hugo Gryn. May he be allowed to rest in peace, and may we, at last, learn to live in peace," he said.
He issued a seven-point list of principles for mutual respect between Jews, calling on them to work together on matters affecting them all - such as fighting anti-Semitism, remembering the Holocaust and improving relations with other faiths such as Christianity and Islam.
Last night there was much speculation last night on the hidden agenda of the person responsible for the leaking.
Dr Sacks would only say: "The leak was a breach of confidence. It flouted the Jewish laws of privacy. It was intended to destroy the relationships of trust essential to communal harmony."
But Matthew Calman, the editor of London Jewish News, suggested the leak was a deliberate "trap" laid for reformists, in order to re-open the divide in the Jewish community.
He said: "We have to ask who leaked this letter and why? The answer to that question is that Jonathan Sacks has made enormous strides towards reconciliation among the different movements in Anglo-Jewry over the last five years.
"The people who leaked this letter are his right-wing critics who despise Rabbi Romain and Reform. It is an attempt to destroy the kind of reconciliation which I know Rabbi Romain and his colleagues are working for."
Yesterday, the "trap" appeared to have worked. In a joint statement the British leaders of Reform Judaism called for a rethink of the post of Chief Rabbi. The statement said: "It seems that, constantly, the Chief Rabbinate is forced into two conversations, embodying two sets of language and two messages tailored to the respective recipients. This is simply not consonant with a community of trust and integrity.
"He says that his whole purpose is to `gain a victory' over us and then calls for peace."