Abe Spector and his sister, Sheri Adolf, children of their mother's first marriage, were traced to their homes in Michigan and told of her death.
They praised the burial society's "amazing" attempts to contact them.
The siblings had not seen their mother, whom they described as "eccentric", for more than 13 years after she disappeared from her US home. She left them no explanation as to where she was going and, they said, turned down their repeated attempts to make contact.
Last week they came to London to visit her grave at the Adath cemetery in Cheshunt, Hertfordshire, and attempted to piece together details from the last years of her life.
Ironically, a relative living in Whetstone, North London, had seen the story about Mrs Kamen's death in the JC earlier this month, but had ignored it, knowing her only as Sylvia Spector, her first married name.
A year after her first husband, Geoffrey Spector, died in 1973, she married Morris Kamen.
Mrs Adolf, who last saw her mother in April 1995, said: "She left and did not tell us where she was going. It was like a person going out to buy cigarettes and never coming back.
"We had tried searching for her and I wrote to the social security administration in the US, but they wrote back and said she did not want to be in touch."
Mr Spector said his mother "just wanted to be alone" and was "not interested" in having her family around her.
"Being buried in England was probably what she wanted. In her own mind she must have known that's what would happen," he said. "We are very grateful, surprised and happy that people tried to find us."
He now hopes to contact other long-lost family who may remember his mother by her maiden name, Sylvia Rutz.
Mr Spector said that being told of the death had provided his family, which now includes grandchildren and great-grandchildren Mrs Kamen never knew, with closure.
An Adath Yisroel official said: "Burial is a big responsibility. We did not know how the next-of-kin would react. It's a good outcome to a sad story."