The oddest of circumstances brought the distinguished Swiss photographer René Burri and me together. Our meeting happened over the mournful grey waters of the South Atlantic Ocean: ever since then I have been profoundly grateful.

Seeking the opportunity of reporting about the Falkland Islands years before the war between Britain and Argentina over the territory we by chance found ourselves in the same unfrequent Argentine air service from the Patagonian port of Comodoro Rivadavia to the airstrip at Port Stanley.

As two journalists seeking to get to know the islands, we fell into conversation wondering what the far-flung settlement at the bleak extremity of the inhabited world would soon be offering us and were making plans for collaboration. We wandered in some battered motor around the bumpy tussocks of grass in East Falkland, whose emptiness is exceeded only by that of neighbouring West Falkland, both of which then were completely and utterly devoid of either paths or tracks and of which today, after the war, they still have very few.

I admired his eye for a picture and his direct ways of composing it. One particular stormy day we were out along the shore, I was wearing a bright yellow waterproof which offered some protection from the driving rain. René draped me in wreaths of giant brown seaweed yards long which gave me a very striking – though not necessarily very attractive – image.

Born in Zurich in 1933 the son of a chef and his wife, he took one of his best pictures with his father's camera when he was 13, capturing Winston Churchill standing in his homburg hat in an open-topped car on a parade in the Swiss city. He continued art studies in his home town. Doing military service in the Swiss army he underwent a sort of apprenticeship taking picture for his unit. He remembered going on exercises using blank rounds and a corporal yelling at him, "Burri, get down, you're dead!"

He soon wanted to escape a Switzerland where, as he said, "there was a mountain every 50 metres." He joined the Magnum co-operative agency in 1956, becoming a full member three years later.

He made his name as a careful and patient photographer, devoid of any trace of pushiness, which would have been alien to his gentle and generous character. Soon his portfolio was stuffed with a host of world famous portraits of great figures, from the cigar-smoking Che Guevara – taken in 1961, Burri's photograph would have made his fortune if it had not been pirated throughout the globe – to Fidel Castro, Pablo Picasso, Le Corbusier and Alberto Giacometti.

He devoted himself not to the instant shot but to a painstaking lifetime of mature work. He recalled how wandering about New York in his twenties he found himself standing beside Greta Garbo in her dark glasses on the pavement. She recognised he was a photographer by the Leica he was holding and smiled, but he decided not to intrude by taking her picture. Later he concluded that that instant had told him than he did not have it in him to join the paparazzi.

He worked in Vietnam and on other battlefields but took great care not to allow war to become a drug for him, as it had done for many of his colleagues. During the Six Day War in Palestine he found himself among a group of Bedouins carrying white flags among burning tanks. He turned and saw a black arm sticking out of the sand and thought what an amazing image of conflict that would make in a magazine. "But I didn't take it," he recalled.

He married twice, first in 1963 to Rosellina, the widow of his late Magnum mentor and colleague Werner Bischoff. They had two children. She died in 1986. His second wife was Clotilde Blanc, with whom he had a son.

HUGH O'SHAUGNESSY