In one of the most interesting and unsettling sections of Alan Cumming's memoir, the actor talks about playing Hamlet on stage in 1993.

Objectively, it was one of the high points of his career, but for Cumming it was also disturbing. The deeper he delved into the part, the more he noticed that he and the character were slipping into the same dark water. In the end, he became convinced that what the play was really about was a nervous breakdown, and he knew it because he was having one too.

There were even times when precise moments in Hamlet's life appeared to parallel moments in Cumming's. At the start of the play, for instance, the prince is sitting in the shadows while his family toast his stepfather Claudius. Claudius makes an attempt to drag Hamlet out of his black depression into the light, and build bridges with his stepson, but the prince is having none of it. "I am too much i' the sun," he says.

Around the same time, Cumming says he had a similar experience in his life. "I remember one evening when a group of my very close friends … went for dinner," he writes. "I sat at the end of the table not talking to anyone, picking at a salad. I had forgotten how to be me. Like Hamlet, I wanted to be absent."

Actors drawing parallels in this way can sound self-indulgent or pretentious but Cumming avoids going over the top, perhaps because he's Scottish and knows not to haver, but more probably because he has a point. Like Hamlet, Cumming did begin to withdraw from life, his friends, his family and, like Hamlet, much of Cumming's unhappiness centred on the relationship with his father (in the actor's case a violent one).

"You can't go through sustained cruelty and terror for a large swathe of your life and not talk about it and be okay," says Cumming. "It bites you on the arse big time." It's not exactly the language of Shakespeare, but he's right.

Not My Father's Son centres mostly on how Cumming did begin to talk about the cruelty he suffered from his father. At the time of his Hamlet, he had started to feel overwhelmed by his family history and it was this that led to his Prince of Denmark depression. As he picked at his salad, he was thinking about what to do, and how he had ended up where he was.

He had grown up in Angus where his father was a forest manager and, because his father was prone to sudden, violent outbursts, learned to interpret his every action and reaction so as to avoid an attack. When the attacks did come, they were visceral and Victorian, and Cumming describes them in language that only occasionally becomes overwrought.

At one point, he tells us that his father thought he needed a haircut and so administered it violently with sheep shears. "They were blunt and dirty and they cut my skin," writes Cumming, "but my father shaved my head with them, holding me down like an animal." There is another little detail that makes the moment even more disturbing: a lone, bald lightbulb hanging from the shed ceiling.

The fact that, after his contemplations while playing Hamlet, Cumming did eventually confront his father, makes you like him. The default position in the British family is to talk about anything except what's causing pain, but Cumming overcomes the pressure to conform. And it works: at the start of the process he says there was not one childhood memory that was not clouded by fear, but by the end of the process, he says "I am okay. I survived."

There are some problems with the book, though. One of them is that Cumming is telling two stories, not one: the story of his father but also the story of his maternal grandfather, whose history he investigated in the BBC programme Who Do You Think You Are?

That would be fine in principle, but instead of relating the narrative chronologically (always the best option unless you are extremely confident and skilled) he chops the story up into slices and arranges them out of time. This means that just as you are beginning to engage with the story of Cumming's father, suddenly the narrative moves from the present to the past or back again.

The other problem is that the tone occasionally slips into over-excitable, especially in the much less interesting sections about awards ceremonies and other show business frippery. Here, at the end of breathless sentences, the exclamation mark makes many dreaded guest appearances.

The disorientating effect of this change in tone, and the time-jumping technique, in the end dilutes some of the book's emotional power, although it does not prevent Cumming emerging as a likeable and sensitive person. And Not My Father's Son does at least try to find a path between those two horrors of celebrity books: the misery memoir on the one hand and the perky chatterbook on the other. Best of all, its emotional intelligence is high. It is thoughtful but it is a warning as well. "The truth can hurt," says Cumming, "but not knowing can hurt more."