The bedroom of the young male musician in 2016, recorded for the future use of pop historians. Six guitars. Three keyboards. Hand-held music sampler. Three pairs of tired-looking headphones. A tube of Pringles, two empty pizza boxes and a bottle of Jack Daniel’s. Shoes, shoe boxes, sombrero. PlayStation and David Lynch collection on DVD. A large book depicting cross-sections of the spaceships from Star Wars. Unmade queensize bed. Archy “King Krule” Marshall – the musician whose bed and bedroom this is – sees me making notes and says: “Don’t mention the jizz rags.”

The 21-year-old sits on the edge of the bed and shares a cigarette with his brother, Jack, 23, a visual artist who has sometimes exhibited under the alias Mistr Gone. The bedroom is in their mother Rachel’s house, on a residential road off the western edge of Peckham Rye in south London. The family has been here for two decades. Archy (an arrestingly Gothic piece of biography, this) was born in the same bed he now sleeps in, the one he’s sitting on as we speak. Jack says he can remember being led inside this room, as a two-year-old, to meet the new delivery. He was confused by people’s use of that word, delivery, and assumed his baby brother was something like a parcel or a pizza. “After a few weeks, I asked, ‘When are you sending him back?’”

Peckham Rye is mythical, mystical. I know people have seen UFOs over it. And I’ve seen at least one ghost there Archy Marshall

The house is clearly important to these eccentric, artistic siblings: it seemed worth celebrating in some way. And so with Archy on hiatus from his career as King Krule – while he’s between albums one and two, 2013’s 6 Feet Beneath The Moon and a still-untitled follow-up – he’s collaborated with Jack to produce a book of paintings, photographs and poems, also an accompanying “soundtrack”, in celebration of their mother’s home and the neighbourhood around it. They’ve called the project A New Place 2 Drown.

Jack takes a proof copy of the book from Archy’s shelf. “All the visual ephemera was done within a square mile,” he says, showing the photographs of central London’s skyline, as viewed from a hilltop suburban estate near their home; also of friends gathered in Archy’s bedroom, or queuing for takeaways in a Jamaican chicken restaurant, clutching flip phones, climbing through spiked fences, smoking fags on Peckham Rye. Some of the photographs are overlaid to the point of inscrutability by Jack’s painting. The brothers were inspired here, they say, by the graffiti culture notion of “buffing out” – that is, the covering up of graffiti by local authorities. There’s a page on which prominent local symbols have been transcribed: underground circle, traffic triangle, McDonald’s “M”. Archy, a great PlayStationer, has messily filled a page with cheat codes for Grand Theft Auto.

His soundtrack that accompanies the book – leisurely, immersive, strange and powerful, like much of his output as King Krule – ranges all over in its subject matter; again, the local area shows its influence in tracks titled New Builds, Buffed Sky, Thames Water. One of the songs, Archy says, explores how having relationships with girls in your community, or inside your immediate friendship group, finally becomes incestuous, as everyone winds up going out with everyone. As for the overarching title, A New Place 2 Drown, it was a phrase that came to him one day while he was sitting on a bench on Peckham Rye. “It was a mad-nice bench. The green just open in front of you. It’s a mythical, mystical piece of land, Peckham Rye. I know people have seen UFOs over it. And I’ve seen at least one ghost there. I was walking down Barry Road and this old, old football got kicked at me. I turned round and saw a 50-year-old man wearing a full Charlton Athletic kit...”

“Mm,” says Jack, frowning.

Watch an introductory video for the A New Place 2 Drown project.

He seems to sense that the thinking behind the project can sound a little vague, however entertaining his younger brother’s riffs, and explains that his visual elements in the book and Archy’s compositions are meant to be experienced together, “like two halves of a puzzle”. The same could be said of the brothers, both redheads, pale and freckled, but very distinct in their manner of communicating. Two sides of the same coin is how their mother puts it.

Archy has a deep voice, his long, rich sentences studded with playground patois – sick as an adjective, vulture as a verb. He tends to speak in exotic, rambling monologues that recall the Morrissey- or Bragg-like verbosity of his debut album. Jack is quieter, more measured, nodding through his younger brother’s flightier declamations and often delivering, afterwards, an ambiguous “mm”.

Their mother, Rachel, calls the boys’ upbringing “a bit off the wall”. She is a tailor and costume designer who recently took a gig dressing 1930s mannequins for the TV drama Mr Selfridge. When Archy and Jack were young, she ran art clubs from the front room. They describe her, back then, as “heavily into R&B, the garage scene”. Jack and Archy’s father lived separately and the boys stayed with each parent at different times. When I ask if this would account for their special closeness, as adults, they say “probably. We were always going between houses together and stuff.”

When he turned 13, Archy started to have difficulties at his secondary in Forest Hill, difficulties, by the sound of it, that stemmed from his never being there. His truancy became so exhaustive that at one point the police threatened involvement. It was while he was “out of school”, he says, that he first started writing music in his bedroom. The habit continued when it was arranged that he transfer to the Brit School in Croydon, the performing arts school where the curriculum skews away from traditional subjects and towards the career building of arty young tinkerers.

Archy and Jack Marshall at home in south London. Photograph: Katherine Anne Rose/The Observer

Archy stopped bunking, kept composing. When Jack formed a band with his friends – “a crazy-arsed punk-funk-weird-lyrics band,” remembers Archy fondly – and started to get gigs in local venues, Archy wangled support slots.

His stage name was Zoo Kid at the time. (Both the brothers are furious adopters and shedders of stage names, pseudonyms, sobriquets... “Didn’t you want to be called Pimp Shrimp for the new book?”) They’re pretty sure their youthful adventures in music led to the closure, about six years ago, of a south London music venue called the Deptford Arms. “Shut down after a gig we did,” says Jack. “Yeah,” says Archy. “Because we filled it with 15-year-olds … I was 15. I remember being at the bar and trying to get a drink and suddenly there were five cops behind me.”

That year, still going by Zoo Kid, Archy released his first (brilliant) single, Out Getting Ribs, through the independent label House Anxiety. Jack, whose interests were drifting away from music and towards visual art, painted the record’s cover. It started them on a seam of collaboration that continued for the next several years, Archy ditching the name Zoo Kid for King Krule, signing to XL Recordings and putting out singles and EPs before that well-reviewed debut 6 Feet Beneath the Moon. Jack provided the artwork for all of it. “I probably wouldn’t have got this far with art if I hadn’t started doing Archy’s record covers,” he says. “That came at a time when I was leaving school. Working out what to do at uni. I thought I might try to be an artist, or I might try to be…”

Archy interrupts. “Didn’t you want to be a lawyer?”

He says this last word with the purest, undiluted scorn.

“International law, yeah. I thought if you did international law you’d be like a superhero. You could do something to help people.”

“It was so random.”

“That was how the family engaged with the idea, as a whole,” Jack says.

“And it only lasted, like, a month,” says Archy.

“Then I got my exams results, yeah. And I thought, ‘Maybe not law.’ I chose art instead. Thought I might as well give that a go. I liked making those album covers...”

When Archy’s career as King Krule began to take off (Vice called his album “a pained coming-of-age masterpiece”, i-D put him on its cover) the family seem to have found the success of the youngest Marshall hilarious. Rachel tells a story about the hair salon down the road – how someone went in not long ago with a picture of Archy as King Krule, asking to be made to look like that, which made her laugh because she’d given him the haircut with a pair of electric shears on a chair in the garden.

Mother and brother were also canny about making the most of an opportunity, however. Archy had been wearing colourful shirts tailored by Rachel during gigs and in photoshoots. Now she started selling them online. Jack, trying to push on as an artist, remembers professional doors opening via Archy. In 2014, the brothers were asked to exhibit together at the Display Gallery in Holborn, Jack providing most of the visual art and Archy a four-hour “soundscape” of music. That show was exhausting work, they say, but they loved collaborating so extensively, thus the present book-and-soundtrack project. Before Archy’s moment fades – should it fade – they wanted to get it out, this quirky, gently indulgent, but absolutely genuine tribute to the home and neighbourhood that shaped them.

Before I leave the brothers – that PlayStation just begging to be fired up – I ask Archy how his label, XL, reacted when he told them he was planning to pause his ascending solo career and spend a year-plus working on an esoteric family art project.

Archy sniffs. “I only speak to the label about once a year. Or not much anyway. They kind of let me do my thing. I know where my deadlines are, and I’ve got to abide by them. But they let me do my thing.” He acknowledges he’s supposed to be well under way on a second album by now. “But I dunno, man. It’s taking a little longer to make. I’m figuring out my guitar sound, changing it… it’s hard to work on one thing when you’re putting a lot of energy into a different creative project. You take ideas from one thing to another. You dampen your other projects by stealing from them.”

Watch King Krule’s video for A Lizard State.

Sitting on his bed, Archy has taken up that handheld sound sampler from among the bedroom’s instruments. It’s a calculator-size thing with buttons that zip and ping and make imitation drumkit noises under his fiddling.

“It’s just not felt right to go and make the second album yet,” says Archy. Boing. Zip. “But I’m starting this year. Yeah. Clean slate.” Boom boom. Ping. Tish! It almost sounds as if he’s starting to compose the record now, as we speak.

Rachel puts her head around the door. She asks if the boys would like anything. Tea? Bacon sandwich? Affirmatives are grunted. New cigarettes are rolled in anticipation. The next album will have to wait.

A New Place 2 Drown (£24.50) is available to order here