It was easily the most fruitful of David Miliband’s efforts to restore Anglo-Russian relations during his visit to Moscow. After a day of difficult diplomacy with his Russian counterpart, Sergei Lavrov, the Foreign Secretary sat down to discuss family history over tea, fruit and cakes at the home of his new-found relative Sofia Miliband.

An exchange of gifts sealed the entente between the youthful minister and the retired academic; he brought a box of tea and Ms Miliband presented him with three ceramic vases — one for his family, one for his brother Ed, and one for their mother. Mr Miliband described his relative as “tireless” and “wonderful” after the two-hour visit late on Monday night. Writing on his Twitter page, he said: “She’s done everything from codebreaking to beat the Germans, to publishing a bibliography of orientalist studies.”

It was the second family reunion for Ms Miliband, 87, who stunned Ed Miliband during his visit to Moscow last month by calling the Energy Minister on a radio phone-in show to declare she was his relative. He visited her twice for what he later called “a very moving and fantastic experience”. The two families have established that the Milibands’ great-great-grandfather, Abraham, was the brother of her grandfather, Osip, in Warsaw, Poland. Their branch of the family went west early in the last century, to Belgium and then to Britain, while hers moved east to Moscow.

Ms Miliband had met the brothers’ father, Ralph Miliband, a Marxist political scientist, at the Lenin Library during a visit that he made to Moscow in 1964. “He gave me his telephone number in case I ever came to London,” she said. Ms Miliband travelled to Britain several times but was unable to make contact before Ralph Miliband died in 1994. By then David was Tony Blair’s head of policy while Ed was a speechwriter for Gordon Brown.

Ms Miliband, a widow with no children, said she had been “absolutely happy” to meet David, 44, and Ed, 39, adding that they had felt instantly at ease. She said: “They have the Miliband smile, so I knew right away that they were ours.”

Ms Miliband survived the Stalin Terror and worked as a Soviet codebreaker during the Second World War before becoming an expert on Iran. Tehran’s nuclear ambitions loom large in David Miliband’s present job — but she insisted that they did not discuss politics.

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