David Miliband has revealed how he and his brother Ed recently accompanied their mother and aunt of a “very moving” visit to Germany after finally learning where their grandfather died.

The paper trail for David Kozak, the brothers’ maternal grandfather, had ended at Auschwitz until this year, when a German historical society made contact, saying it had traced Kozak’s death to a small concentration camp near the southern town of Hailfingen.

“It was important for both of us that we went on this visit with my mother and our aunt,” said David Miliband, speaking the The Sunday Times magazine this weekend. “It was very, very moving.”

Their mother Marion and her sister Hadassa were separated from their father at a young age and were sheltered by local Poles. Kozak was one of 43 members of the family killed during the Holocaust.

David, who was foreign secretary under Tony Blair, left politics in 2010 to head up an American charity after his brother Ed fought him for the leadership of the Labour Party. Ed secured victory by offering concessions to trade unions, but the nature of the brothers’ battle left deep scars, and the two barely spoke for years.

David, whose views were considered more centrist than Ed’s, this week took aim at current Labour leader Jeremy Corbyn for his record on antisemitism, asking: “Why ever say this is overblown?”

He added: “It’s so disgusting that you’ve just got to be really vigilant. If there’s prejudice against Pakistanis, you call it out – you don’t just say ‘All racism is bad.’ It’s got to be called.”