I've been looking forward to this," says Archy Marshall. "They told me it'll be like psychiatry – like counselling." The artist formerly known as Zoo Kid, DJ JD Sports and Edgar The Beatmaker smiles broadly, takes delivery of a pint of Kronenbourg and rolls the first in a long series of gaspers. These days, Archy goes by the name of King Krule. "Imagine a king crawling through the city on his hands and knees," he explains. "It's aristocracy at the very bottom."

In front of Archy sits a double-vinyl pressing of his remarkable debut album, 6 Feet Beneath The Moon, and during our hour or so together he simply can't leave it alone. For someone who has no real recollection of life before MP3s, the physicality of the thing clearly makes Archy very happy indeed. "I do love the music aspect of the internet," he says. "The internet made me. But I also love the fact that the internet really fucked the music industry. I come from a punk vibe, so if you can illegally download my album, fuck it, do it! I illegally downloaded all of my music.

"I couldn't give a shit about MP3s," he says, perhaps unexpectedly for someone managed by the same chap who looks after Adele. "But if you buy my vinyl, I'll be happy, because this … "

He picks the record up and flips it over.

" … is a fucking masterpiece of craft and art!"

The first time you listen to King Krule you'll be shocked by his rich, angry baritone – a pissed-off Joe Strummer having a stand-up row with Billy Bragg, a voice that seems absurd coming from this pencil-thin, hollow-cheeked boy. The second time you listen, you'll be gripped by the beauty of his songs – even though, first time around, you didn't think they were beautiful at all. Initially, Ocean Bed or Bathed In Grey are all elbows and needly fingers, wavery bark and bite, but hear them again and a testy, tarmacked elegance is apparent. Archy's real talents become clear when, on the gorgeous Nelson Riddle-era Sinatra howl of Baby Blue, he croons, "My sandpaper sight engraves a line into the rust of your tongue". And then, sounding like Chet Baker with a penetrating head wound: "Girl, I could have been someone … "

It's worth remembering at this point that Archy won't be 19 until the day this article appears. "Well," he laughs, "I listen to a lot of jazz standards, like When Your Lover Has Gone [Einar Aaron Swan's 1931 composition, later covered by Sinatra]. That's got really simple but very, very effective lyrics that talk about being depressed and seeing no beauty in life because your lover's gone."

Meanwhile, in your song, you're staring so intently at this girl you're scarring her? "Yeah, I'm scarring her tongue, her lust, her mouth." He lights a new smoke. "I actually find a lot of pleasure in writing lyrics."

When the Guide first interviewed Archy almost two years ago, he was a little bit prickly and aloof – an impression reinforced by those brilliantly acerbic lyrics – but that can probably be attributed to typical teenage bravado. Today, he is fantastically entertaining company. He has been through some incredibly painful times, and fully expects to experience more, but is open and honest and unafraid to talk about any of them.

It's nearly three years since he released his first single, Out Getting Ribs, on the tiny House Anxiety label. He's been at the centre of a blizzard of activity ever since, even while his old manager – his mum – tried to hold everyone back a little and carve out some space for her son to be a normal teenager.

King Krule. Photograph: Sarah Lee for the Guardian

Except, of course, there's nothing remotely normal about him. Normal teenagers don't have Frank Ocean singing their praises and proposing collaborations ("His new album's fucking good," says Archy. "That collaboration will happen when it happens, y'know?"). Normal teenagers don't write songs like Cementality, which moves with the grace of Gil Scott-Heron while considering the pros and cons of throwing yourself out of a window ("It's about killing myself," he confirms. "Becoming one with the cement"). Normal teenagers don't enthuse at length about the Damned, Josef K, New York no-wave movement anti-heroes James Chance, DNA and John Lurie, pianist Bill Evans and jazz singers Blossom Dearie and Nancy Wilson. And when asked about their heroes, normal teenagers definitely don't hold up Ian Dury, Fela Kuti, Eddie Cochran and Malcolm Owen from the Ruts (Archy's mum once dated the band's drummer).

Archy grew up shuttling between his mum's house in East Dulwich and his dad's flat in Peckham. He describes the former as a working-class environment, the latter as more middle-class. "My dad was fucking strict," he says with a smile. "He wouldn't let me swear. But my mum would let me do anything. Dad was more … brown rice." He says he went through "a lot of fucking weird shit" when he was young, most of which he insists his dad has no idea about. At the age of 13, after refusing to go to school, he was first given a home tutor, then sent to two education centres for permanently excluded kids, which he has since described as like being "thrown into the lion's den".

Meanwhile, he was getting tested for various types of mental illness at London's Maudsley Hospital. "That really took its toll on me. It was then I decided to not give a shit about the establishment, because a lot of the time, the doctors and the psychiatrists and the counsellors and my social workers were plain wrong. Basically, I hated everyone."

Social services threatened Archy's parents with prison terms if they couldn't get him to school, but still he refused to go. His mum would have to call in his dad, who'd physically pull him out of the house and take him there. Eventually, though, Archy's love of music provided an escape.

During bouts of insomnia, he recalls lying awake deep into the night listening to Pixies and the Libertines through his grandmother's big Sennheiser headphones. "That was when I began to think about creating soundscapes," he explains. He won a place at the Brit School, and although he struggled with the discipline at first, he began to love the place. "It's a really good school and I learned a lot. A teacher called Derek Moir taught me to love history and sociology, and that all really helped me out." He takes delivery of a fresh pint and brushes tobacco from his LP sleeve. "I know my story sounds terrible, but I wouldn't change anything in my life, because it all helped to formulate what I feel now is a very strong mind."

Sometimes it's very obvious that Archy is still a teenager, like when he gets worked up about an old girlfriend who shared with other people the music and art they had listened to together. That doesn't seem like much of a crime? "Maybe," he replies, "but mine is a very cynical mind."

At other times, though, he comes across as wise and insightful. In 2011, Archy had a revelation: he didn't want to end up being 30 and still known as Zoo Kid, like some ghost-stepping Angus Young, pulling on the Burberry cap and pretending to be a teenager – to feel like a teenager – for ever more. "I'm not going to lie," he laughs, "I've never referenced that before, but that is exactly what I pictured – me as the guitarist from AC/DC, yeah. Fucking hell!"

He noticeably brightens as our "therapy session" comes to a close. "I think I've become really positive this year. I've got rid of a lot of cynicism and anger. I feel positive about my development and I just want to carry on making music and building myself as a person. Now I want to be a 30-year-old, y'know?"

What sort of 30-year-old? "I'll be fully suited-out," he smiles, holding his arms out wide, "with all this vinyl I've created." You're ready to create a huge body of work? "Yeah, man, because not enough people do that nowadays. I want to get more and more sophisticated. I'm ready to go from being a kid to being a king."

6 Feet Beneath The Moon is out today