The family says they are now facing the loss of their “emotional and community anchor” on Hackney’s Linzell Estate, where they have lived since 1978.
Their mother, Megan, died in July after a short illness with cancer.
The siblings have said their grief has been compounded by delays to her burial, which took two months, and by Ms Thompson losing her job at Santander.
“It’s so close to Christmas,” Mr Gray told the Local Democracy Reporting Service.
“They haven’t actually shown us proof of the earlier succession,” his sister added. “I just want clarity.”
The family may receive a discretionary offer of succession or be rehoused, but Ms Thompson said she has not had anything in writing and is frustrated by “vague” conversations with housing officers.
She said: “A lot of other people have lived here for a very long time. My daughter has just started school here.”