“I still have a fear that it’s all going to be taken away and I’ll end up in poverty again,” he said in a clip from a new Channel 5 documentary, How The Other Half Live, airing Thursday (November 17).
“It never leaves you. It’s like the Damoclean sword that hangs over you throughout your entire life.”
The actor has hosted the two-part show, which explores the wealth gap between the rich and the poor.
It also addresses his own complicated relationship with money, which he describes as his “own personal demon”.
“I never really felt it much when I was young,” he explained. “I was a kid and just got on with it, I was literally surviving.
“But, as I got, older I’d look at that boy and think, ‘My God, he survived, how did he do it?’ It’s still a mystery to me.”
The Golden Globe-winning star also revealed that, after his father died, his mother discovered his bank had “the sum of £10 in it. We were destitute”.
He continued: “My mother only had a widow’s pension, which would often run out before the end of the week.
“I’d go to the fish and chip shop and ask if they had any scraps - the bits of batter at the bottom of the fryer - and take them home for us to eat.”
Cox, who co-created the hit HBO drama Succession in which he plays billionaire media mogul Logan Roy, wanted to investigate the growing wealth gap in his native country and the US.
The documentary takes him to the impoverished Dundee home where his father died prematurely, which led to a difficult childhood that included his mother’s breakdown.
Cox, who left home when he got a grant to study acting at renowned drama school LAMDA in London, also visits the affluent parts of Miami, and the soup kitchens of New York.
He said: “Wealth is becoming more concentrated in that top one per cent and the rest of the world is suffering.
“When you play one of the richest men in the world, you live that life for nine months of the year, where you’re in a kind of cocoon, and I feel there’s an inequity that needs to be dealt with.
“So this series comes very much from what I grew up with and what I saw, having been lower-middle class and having a relatively happy childhood until my father passed away.”
When Cox, who has an estimated fortune of £12.5m according to Celebrity Networth online, was challenged as to whether he has become “one of them”, he said: “Well, I’m not. I’m doing well but I am not one of them. I’m not a multi-millionaire, I am not Logan Roy!”
Brian Cox: How The Other Half Live airs on Thursday at 9pm on Channel 5