Burnham has spoken about his father's illness, which meant that he didn't know his son had become prime minister.
The experience is one of the driving factors in the Burnham's aim to reform the social care system.
In an interview with The Times on the eve of taking office in July, Burnham revealed the extent of his father's illness.
He said his father was unaware that he was on the brink of power.
"That's a sadness because he would be (proud)," Burnham said.
"The way I look at it, it's his achievement as well.
"A whole family achievement although he doesn't know it."
In a major speech about reform of social care later that month, Burnham promised to help "my dad and the millions like him" faced with the unfairness of the system.
Burnham's father was a former telephone engineer, first with the Post Office and then with BT.
Burnham's described his "close-knit" upbringing in the 70s and 80s in his book Look North, paying tribute to his parents.
"Their approach was one of quiet encouragement and confidence-building. Our family home in Culcheth was always full of music, life, laughter, love and support."
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