In the garden of his home in the Orthodox Jewish Israeli West Bank settlement of Tappuah, Lenny Goldberg rubbished the idea that it was us Brits who made modern Israel possible. “The only reason we have a country here,” he told Jane Corbin, “is not because of the Balfour Declaration. It’s because Jews sacrificed themselves with blood and fire and bullets.”

Goldberg, a tough New York Jew turned tough West Bank settler, is among half a million Israelis living in 140 towns and villages that have sprung up on the ostensibly Arab West Bank in the past 30 years. When Corbin told him that these settlements were illegal according to international law, Goldberg replied that he didn’t care about mere secular laws. He was interested in the word of God as expressed in the Bible and that, according to that higher authority, there is no Palestine and so there can be no question of Arabs having a claim to live there. “This is where Abraham walked. Why should we give it up for a bunch of murderers?” he asked rhetorically.

Corbin, who has been covering the Arab-Israeli conflict for 30 years and so, you’d think, has had to become virtuosic with the journalistic poker face, didn’t contradict him. And yet, the thrust of her terrifically engaging programme was contrary to Goldberg’s intolerant vision. Corbin’s sense in The Balfour Declaration: Britain’s Promise to the Holy Land (BBC2) was that the 67-word document written by Arthur Balfour 100 years ago tomorrow enabled Zionists to realise a 2,000-year-old dream of returning to the Jews’ promised land and that, what’s more, it contained a beautiful dream of co-existence between Arabs and Jews.

The declaration, she noted, included not just His Majesty’s Government’s commitment to the establishment in Palestine of a national home for the Jewish people, but also this extraordinary clause: “it being clearly understood that nothing shall be done which may prejudice the civil and religious rights of existing non-Jewish communities in Palestine”.

What was even more extraordinary was that it was one of Corbin’s relatives who added that clause. Tory statesman Leo Amery intended it to safeguard the rights of Palestinian Arabs when, as happened during the 1920s and 30s, Jews arrived in their hundreds of thousands to live in British-mandate Palestine and fought for the creation of the Israeli state in 1948. As a child, Jane’s mum, Olive Amery, would tell stories about Leo, whose Jewish mother brought her son up as a Christian, and who grew up to become not just an Islamic scholar but also served as colonial secretary during Britain’s mandate years.

What followed was a well-judged, if grim, primer of a century of Palestinian-Israeli history. It was one which, if you’re British, could only make you contemplate the middle distance with rueful mien. In 1939, for instance, the British bowed to Arab uprisings and cut back Jewish immigration – at the very moment when Jewish refugees fleeing Nazi murderers needed a safe home outside Europe. Amery himself was responsible for cutting back on British forces in Palestine as Arabs and Jews fought each other. Had he not done so, Corbin mused, perhaps the bitter tragedy of recent years could have been averted. But the British have always been hopeless at solving problems that are their own fault – think Iraq, Ireland, Brexit and, perhaps, Israel.

At one point, Corbin unfolded a map from the Central Zionist Archives. It depicted her relative’s 1946 Amery Scheme which envisaged a two-state solution that, Leo thought, was the best hope of keeping his humane clause of the declaration alive after a decade of Arab-Jewish fighting over the future of Palestine. In it, the red patch extending from the sea represented the Jewish state, while the blue splodge extending westwards from the Jordan River represented the Arab state. There was also a buff coloured patch called the Jerusalem Zone that could be, apparently, under international rule.

That dream, like the Balfour Declaration, never became reality. The Arab State that Amery sketched on the map is now dotted with Israeli settler villages like the one where Lenny Goldberg lives. And Jerusalem is an Arab-Israeli flashpoint.Corbin was at her best in tracing what went wrong after the Oslo accords in the early 1990s that seemed to promise Balfourian peace between Arabs and Israelis but foundered only a year later, after the murder of one of the agreement’s great architects, the Israeli prime minister Yitzhak Rabin, by an Israeli ultranationalist. She visited the abandoned Palestinian parliament building in Abu Dis, East Jerusalem. It was here that, as a result of the Oslo accords, PLO chairman Yasser Arafat was to have had an office overlooking the Dome on the Rock, the Islamic shrine on Temple Mount. The building, a symbol of Oslo’s dashed hopes, has never been used.

Instead, Corbin’s subsequent career has involved bearing witness to Palestinians and Israelis collapsing into deepening mutual loathing. All this made Corbin’s conclusion seem wildly optimistic. She argued that violence is not inevitable in this part of the world and that the dream her relative argued for 100 years ago might yet be realised. I wish I could believe that.