Lord Jonathan Sacks has a style that addresses his Anglican listeners and at the same time addresses his Jewish audience.
Jews generally speak of Torah, avodah, gemilat hasadim; or God, Revelation and olam haba; or God, Torah, and Israel; and now creation-revelation-redemption. All sets point back to Torah.
Christians use the words witness, mission, covenant, proclamation- all about good news to be brought to the world. “witness.” in their reading of Israel’s covenant history: means the proclamation and exchange of views held with conviction.
Jonathan Sacks has discussed “witness” as a theological concept in almost all of his books.
In his 1992 Crisis and Covenant, he writes, “An early rabbinic commentary put the point audaciously: ‘ “You are My witnesses, says the Lord, and I am God” (Isaiah 43:12)” (28) In this work he uses the word the way Emil Fackenhim does, we as witnesses to the destruction of our people in the holocaust and now we give witness by the survival of the Jewish people. Our news to the world is the survival of the Jewish people.
In 1997, he writes “Somehow the Jewish people would be the people in whose daily lives the will of G-d, and in whose collective history the presence of G-d would be particularly evident. You could look at Jews and see G-d. In that magnificent phrase in Isaiah: “you are my witnesses, Isaiah 43:10, says G-d and so it happened.” Jews are witnesses to God’s existence.” This is a Jewish version of the Christian doctrine of the witness; Jews point to God and the original revelation to humanity.
But Jews usually assume the verse talks to Jews about their own redemption As examples, Rashi explains the witness as Abraham and Jacob testifying to their promise for Israel’s redemption and Radak explains that the prophet testifies that just as Sanherib was destroyed so too all of Israel’s enemies will vanish and Israel will be redeemed. Or the use of it for the haftarah of Bereshit is that just as God created the world he is true to his promise to redeem Israel.
A decade later in his Dignity of Difference, Sacks writes “ But from here on he will focus on one family, and eventually one people, to be his witnesses and bearers of his covenant.”(52) The argument is that undifferentiated pluralism leads to totalitarianism, but God chose a single people, the Jews, to teach the world that each people is unique and that there is a pluralism of diversity of different peoples. But the locution is more Christian, Jews are to witness and bear the covenant of Gods’ designs.
None of the Jewish commentators ad loc interpret it in that direction
In his Heal a Fractured World, he writes that we witness to God “not by seeking to convert those of another faith, but simply by reaching out to embrace the image of God in another human being, by seeing the image of God in another human being (47) We have Levinas adapted as an answer to the Christians who seek to convert those of another faith.
Finally, in his recent siddur “The Jewish people … have … been singled out for the most exalted mission ever entrusted to mankind: to be witnesses, in ourselves, to something beyond ourselves: to be God’s “signal of transcendence” in a world in which his presence is often hidden (Siddur p. xxiv).
Jews have Mission to mankind for the presence of God. Hmm… I did a quick online check of the 19 letters to see if Hirsch used it that way, and from my quick check of 19 Letters- Rabbi Hirsch limits witness- Edut to contexts of duty and service of mankind toward God. God is know through the natural order, duty is the Jewish message. I need to check other works of Hirsch and Hertz. But here in Sack’s prayer book the very knowledge of God is the Jewish mission. Is this more Anglican or Jewish?
Update
I checked the commentary of Dr Mendel Hirsch on the Haftarot (called by most people as the commentary of the father) on the relevant verses in Isaiah. Dr. Hirsch comments that only man has will to act on a higher calling of righteousness. Only through zedek will people realize the nature of reality consisting of freedom from material slavery in order to live in happiness and freedom. We are a light to the nations when there will be righteousness in the governments. The concept of witness is that the proof of every historical fact rests , on people who were there, on tradition The Jewish people have witnessesed the rise and fall of the nations around them. You were all at the going out from Egypt, which proves a world of providential care. You are witness to your revelation becuase you saw God’s hand in history.
Hmm..Hirsch does not seem like Sacks. I will check the essays if I get a chance.
The Book of Doctrines and Opinions: 
While on any given detailed point you are right that R’ Sacks is interpreting the texts in a way that differs from the the classical commentators, it seems like he is merely recasting the notion of being an אור לגוים in terms that his Anglican audience will understand. R’ Hirsch and others understood the notion of being a light unto the nations as actually communicating something to the nations, though that communication need not be a conscious, direct one.
Still, I do find that R’ Sacks’ witnessing or testifying may echo the doctrine of being a light unto the nations.
For further related discussions, see Rabbi Sacks’ new Covenant & Conversation, the first collection of his essays on the weekly Torah portion,
Sheryl- Are there passages in the new volume that directly relate to witness? Do they help explicate the obscure locution- witness?
I agree with Arie on this one.
Rabbi Sacks was educated in a classic English framework, so it would make sense for his to use their language to express his ideas, especially as he is always also speaking to the non-Jews.
Perhaps the position of English Chief Rabbi is unique of his role in the larger English society. In Americac do we not have a parallel. Though Rabbis Arthur & Marc Schneier & Shmuley Boteach have attempted to fashion such a role. I am curious about the language that Yechiel Eckstein uses in speaking to the American Evangelicals.
But does recasting “Ohr Lagoyim” as “Witness” change or transform the term?
Also, is this a specifically post-Holocaust move. The survival of the Jews after the Holocaust, a way of doing post-Holocause theology without doing post-Holocaust theology. Does Wiesel also use the term Witness?
Wiesel uses the term is a Sartre way as a courage to give testimony to the difficulties of life. I have the passages collected if you are interested.
Yehiel Eckstein has a unique double covenant theory, where we witness the Christians as the Biblical path for gentiles. (I also have these collected).
Witness is not the same as light to the nations. The former is a closed message witnessed by a closed group and then offered to the world, while the latter is a universal idea.
Rabbi Hirsch is always the latter. Wiesel is not using the word in the same manner.
And this is my discomfort to find Sacks closer to Eckstein than to Hirsch.
I am not certain that I understand the difference that you present correctly.
If I understand you correctly, this Witnessing is a way of dealing with assimilation and maintaining group identity, while simultaneously keeping an “openness” to engagement with the larger culture.
However, the sociological reality in England, where there is still a distinct “Jewish Church” presumably affects how Rabbi Sacks views & presents his role in society.
America is very different. Though, 19th Century Germany was much closer to England than America, but Hirsch, presumably, did not have the same relationship to the German Churches.