In November 1933, Germany brought into effect the Schriftgesetz, an editorial act forcing anyone working in publishing, including photographers, to supply proof of Aryan heritage. It became forbidden for Jews to take photographs on the street. Russian-born photographer Roman Vishniac, first given a camera for his seventh birthday in 1904, was undeterred.

In one shot (Berlin, 1933), Vishniac’s young daughter Mara acts as the apparent focus of the picture, while on the wall behind her a large political poster for Hindenburg and Hitler reads, ‘The Marshal and the Corporal: Fight with us for Peace and Equal Rights.’

A group of children play casually on a Berlin street. In the background, fluttering from a building, a flag emblazoned with a swastika.

Children, in contrast with their relative powerlessness in real life, are astonishingly powerful in photographs. Their unselfconscious charm – the way they stare unabashed into the camera lens – and their vulnerability draw us in. One of the most poignant prints is that of Sara, under-nourished, sitting up in bed in a basement dwelling in Warsaw. On the wall behind her we see some flowers painted there by her father. This glimpse of an attempt to bring a small spark of joy to wretched conditions somehow serves to make it even more unbearable.

But this is not a one-note exhibition documenting Jewish misery; it is intensely involving, surprising, multi-textured. Alongside photographs depicting lives of crushing poverty and despair sit images that are playful and full of vitality — a man seated by a wooden structure containing a mock udder, learning how to milk a cow; a shot of polar bears in Berlin zoo taken from behind the bears so that it is the people beyond who appear caged. In one of my favourites, a gaggle of Jewish schoolchildren practically burst out of the frame, their faces lit up with life.

For the first time, this major touring exhibition has been split across two sites: the Jewish Museum and the Photographers’ Gallery, both in London. Each exhibition is self-contained: the whole story of Vishniac’s work unfolds in each venue — Jewish life in the Haim before it was extinguished by the Holocaust, the rise of Nazism in Germany, Berlin in ruins after the War, American immigrant life, Displaced Persons camps — but if you can see both, I urge you to do so.

Viewing the part of the exhibition at the Photographers’ Gallery, I am almost struck dumb by the intense, direct gaze of a print of a bearded man in a traditional black hat. The beadily intelligent look of those dark eyes is so very like my late father’s (though his beard was rather more modest in dimensions). In his later years, my father (Times cartoonist Mel Calman) took to wearing a black fedora — not because he’d suddenly become more religious but because it looked rather stylish and his girlfriend had protested at his previous choice of winter headgear, a tweed cloth cap.

Then it made me realise just why this exhibition is so affecting, so powerful. It’s that sense of connection. It’s not just as if I am looking across time and space into glimpses of other people’s lives, lives remote from my own; I feel as if I am seeing a dark mirror of the lives my own forebears might have had before they emigrated (from Lithuania and Russia), lives my father and his brother and sister might have had if they hadn’t been lucky enough to be born here. I emerge, blinking into the sunlight, profoundly moved, profoundly grateful to be here.