The phone rings, one of those telephones from my childhood, with a curly wire connecting the receiver. A stripy-shirted arm reaches for it tentatively. “Hello?” says a voice – deep, aristocratic, lugubrious and woozy, but unmistakably Benedict Cumberbatch (confirmed when the camera eventually looks higher). There is a delay and an echo on the line (remember that?). Sad news from New York: his father has died.

Patrick Melrose, the character Cumberbatch is playing, sinks slowly towards the floor, but not in grief. He has dropped something; a syringe. There is a tell-tale blood spot on the shirt, too.

After hanging up, Melrose’s face slowly – very slowly – transforms. His eyes close, he exhales through his nose, the corners of his mouth twist into a smile, because heroin is now flooding his brain cells and because of another kind of release – from the abusive relationship and trauma that was instrumental in getting him mixed up with serious drugs in the first place.

“Old bastard’s only gone and died,” he says to one of the women in his life. He is thinking of giving up drugs, he tells another. Then he Concordes across the Atlantic, where he fails spectacularly to give up drugs (to heroin add amphetamines, quaaludes, valium and alcohol) and very nearly fails to pick up his father’s ashes. He only just fails to kill himself, too.

The first episode of Patrick Melrose (Sky Atlantic), adapted by One Day writer David Nicholls from the autobiographical novels of Edward St Aubyn, covers two days in 1982 in New York, with flashbacks to a miserable childhood that is explored – excruciatingly and poignantly – in future episodes.

It could have been ghastly – messed-up, Tennyson-quoting toff throws money at people and takes a lot of drugs in 80s New York, because his messed-up toff daddy wasn’t very nice to him. And how can the thoughtful wit and exploration – of the character and of addiction and privilege - of the books translate to the screen?

It is a triumph, though. Nicholls must take some credit for managing to boil down five books into five hours of television without losing flavour. I have seen three, each of which has a distinct character that has a lot to do with where and when it is set, yet they nod to each other and belong together, like movements in a symphony. The dialogue (much of which is Melrose in conversation with himself) is sharp; this is tight, intelligent adaptation.

Then there is Edward Berger’s direction. Berger, who did Deutschland 83, does excellent New York 82 as well. There are so many glorious scenes in the first episode. At the funeral parlour on Madison (“only the best or go without” Melrose’s father would have said), where Melrose goes into the wrong room, a Jewish wake, before finding the right one and unwrapping his father like a birthday present (“Is it Dad? It is! It’s just what I wanted, you shouldn’t have!”). A disastrous date with an ambitious New York socialite who doesn’t want a quaalude or even a drink. Another drink with a woman who witnessed some of Patrick’s tragic childhood. During this one, a quaalude hits and everything slows down, as if all the batteries have suddenly gone flat – Patrick’s voice, the movement of the camera … until he does a line of speed in the loo. Suddenly, everything – jerky camera movement included – is on full charge again. It is an immersive experience: not just watching Melrose, but kind of being him as well.

Which brings us to the man who has thrown himself into Melrose. There are other fine performances: Sebastian Maltz, haunting as young Patrick; Hugo Weaving as his monster father; Jennifer Jason Leigh as his wasted, spaced out, waste-of-space mother. But this is the Cumberbatch show and it has come to town.

He had always wanted the part, he told the Radio Times, which might have been problematic, made it a vehicle for his talents and range: look at me acting, now shower me with awards.

Maybe there is a bit of that going on. But it also means he has a deep understanding of the character. He hits just the right note: hilarious, but also tragic, irritating, exasperating. It is addiction personified, sympathetic without being celebratory or glamorised. So, do look at him – it is impossible not to – and shower him with awards. He is, and it is, brilliant.