In a London pub garden, everything is still. It's one of those crisp afternoons, somewhere between winter and the deep blue of summer skies. The faint sound of children darting around playgrounds is perhaps the only sign of life rattling on outside the walls of The Gowlett Arms. The scene's idyllic, like a still-paradise somewhere in SE15 – an ideal interview location. That's how it seems to me anyway. Then again, I'm the interviewer and not Archy Marshall, King Krule, the subject.

The last two options are stupid of course. The release of new album The OOZ, Marshall's first in four years under King Krule, has provided a rare opportunity to speak (or not to speak, as it were) with one of this generation's best songwriters. Leave now and he could be gone for another half-decade. So we crawl slowly forward: I edge toward actual questions, Marshall grumbles about not being able to get a seat when he comes to this pub in the evening. Then comes the blunt, discontented and shrugged-off kicker: "I want to leave London." Really? "Yeah. Everything is done here."

Conversation doesn't run dry, because it doesn't begin. Did you have a heavy one last night, then? "Fairly"; What did you do? "Saw Fazerdaze"; How was that? "Good"; – rinse, repeat and sit in the lingering silence after each short answer. With his sunglasses off now, Marshall's eyes remain fixated elsewhere, unreadable and distant. Maybe he doesn't like small talk? Perhaps he's just hungover? Would he like a stronger drink? Should I leave? Might we be able to do this at a better time?

We'd planned to meet in East Dulwich, southeast London, at the childhood home Marshall shares with his mother (he was born there 23 years earlier, in the room he still sleeps in). But then came the warning sign: a message saying Marshall would be late and prefered to speak at the pub. Somewhere between an hour and two later he arrives, sunglasses strapped to face, pint of tap water in hand, roll-up cigarette prepped and waiting.

The desert, he says, his voice low and heavy. Specifically "Dungeness – the only desert in Europe," located in southeast England, to "start something fresh". Why there? "I don't know. It looked good." Okay; change of tack. How did you find out about the place, then? Slice of pizza now in hand, it seems we finally have lift off: "I guess I went there as a kid. In the 60s a load of painters went there and started a movement. It just looks good. There's an old train line that goes out into the middle of nowhere. "

Born to artistic parents (a tailor and costume designer mother, art director father), an urge to create is practically hardwired into Marshall's DNA. As years floated by since the release of his debut album, it seems those aspirations have become muddied with frustration. If 2013's 6 Feet Beneath The Moon detailed the beginnings of Marshall's journey, third album The OOZ is the moment he becomes submerged in all the heavy gunk – the end product a result of writer's block, the demise and birth of several relationships and the changing landscape of a city crumbling under his feet.

Despite his foundation in southeast London – lived here all his life, references the place in songs and music videos, semi-regularly still plays small pub shows, most recently in Peckham's DIY Space – no single location really epitomises Marshall. The topography of his music is a potpourri of dense spaces above and below the earth : debut album 6 Feet Beneath The Moon, in the "Ocean Bed" or on some "Neptune Estate", A New Place 2 Drown – dark, black and blue canvases of nothingness on which he paints his words. The name of the first album, Marshall says, was a metaphor for aspirations. "You physically always look up [at the moon]. But you can't touch it, it's always there, hanging over you. I guess it used to haunt me."

The title of The OOZ first came to Marshall years earlier when, as Zoo Kid, he created a band with his brother and Jacob " Jerkcurb " Read called Dik Ooz – a name "that was pretty perfect because we were all adolescents and our dicks were all oozing", Marshall jokes. Next up was the art exhibition Inner City Ooz – a wordplay on Marvin Gaye's "Inner City Blues" – which took place in central London in 2014. This time around The OOZ signifies the unconscious growth we all go through when forcing something out, whether that's an art project, music or even emotion.

That track takes the form of two interludes on The OOZ, one of which is spoken by Marshall's father. Originally "Bermondsey Bosom" was going to be seven minutes long, the soundtrack to a walk Marshall would take, winding along next to a railway track, from his previous parent-free home in neighbouring Surrey Quays toward Peckham. Speak to Marshall about anywhere in south London and he has a story. The Bermondsey trading estate where he recorded his album ("I was trying to get a space there but most of the places doubled the rent as soon as they found out I was a musician… the council are fucking up that area"). Brixton ("What Network Rail did there is disgusting). Peckham Rye ("I've seen three ghosts there, I feel"). He remembers getting arrested atop Nunhead Reservoir, a fenced-off area offering views of the London skyline that was once "a place of the underclass, the underworld" and has since become a littering ground for Goldsmiths art students and their tins of Red Stripe.

Everything about The OOZ suggests Marshall's period of growth involved getting lost, becoming buried. The album opener sees him "sinking lower and lower in Biscuit Town" – a nickname for Bermondsey in south London. From time to time Marshall emerges, howling at the moon, but even these moments are tinged with the tonality of a record that spends its time in a state of disrepair, misdirection, frustration, anger. The lyrics are telling: "Nothing's working anymore" ("Slush Puppy"), "I don't trust anyone, only get along with some" ("Vidual"), "My head's in all kinds of mess" ("Lonely Blue"), "I'm not here" ("Sublunary"). Part of this might come from a relationship described across the album, other parts seem to come from southeast London more generally which, alongside "Biscuit Town", is also referenced on "Bermondsey Bosom".

It was nighttime and Marshall "stupidly" stumbled into the policemen who had found their way inside. "One of them said to me..." – he puts on an affected accent – "'here's a bit dangerous, I can't believe anyone can get up here, it must be great for terrorists'." "'Why's that?'" Marshall asked. "'Oh, cos you can see the whole of the city.'" He laughs. "I was like 'You idiots. You've got access to the entire water supply.' There was that famous story about Damien Hirst and all the Goldsmiths students in the 90s going up there and trying to put ounces of MDMA into the water supply. That would be fucking hilarious, walking around these ends and everyone would be fucking pinging, washing in MD."

Marshall has a self-confessed fascination with history and it's on this topic, not small talk, that he seems most comfortable. After discussing a recent trip to Czech Republic where Marshall, his mother and then-girlfriend visited a church with "these huge tombs [made] out of skulls and chandeliers out of hip bones and femurs", talk turns to the debut single from The OOZ, "Czech One" , and its music video. The Frank LeBon-directed visual sees Krule both above and on the ground – a visual metaphor, Marshall says, for a dream-like state. For reasons that will become clear by the end, I've included his response and subsequent frustrations in full below.

I get it though. From a fan perspective… someone's going to be excited to hear you've worked with someone else. I guess it shouldn't always be a story though. I think the story is just fucking funny as hell. When all of us the next day had all of our press photos put together… that was the dumbest shit ever. I don't know… That's how I see some of that sensationalist bullshit. Some of these websites are acting just like tabloids, copy and pasting articles and literally going, 'Now our website has covered that.' It's just a lot of bullshit.

For you guys, I guess that's it: making music. But when journalists hear you've linked up we can get hyped. People love these Pokemon style collaborations. Like: 'Oh shit, he worked with him', 'I wish these guys would work together.' I like working on my own.

You did something with Warpaint, Jagwar Ma and Earl Sweatshirt at some point too, right? Or was that music publications blowing it out of proportion? The thing with music publications and these websites is they'll take a quote or something and make it into a really pointless two-paragraph article. We were all on the same line-up for a festival so we were all hanging out anyway. I'd met Jonti [whose studio it was] maybe two or three years before that in Japan. It was an all-night festival that went from 5PM one day to 5PM the next day, so there was bands playing at 8 in the morning. I got to the studio kind of late, I think everyone had left by the time I got there, it was just me and Thebe (Earl Sweatshirt). So me and Thebe played loads of music. Every time we've made music we've just jammed, we haven't really spoken about it I guess. When he came and stayed with me we were just making hours of music.

It's like a devaluation of writing – every website is guilty of it.

It's just out of context, man. I even saw that thing from an article in the New York Times – and I don't read my interviews, because I hate the way I sound.

Why do you hate it?

I like saying it. I like talking to someone. But when it's put down in print it's a completely different thing, y'know. You don't get tonality, you don't get sarcasm, irony. You don't get half these things. People read it for black and white. So personally, I don't like reading that shit. But already someone said something about Kanye. It's like, look man: you're kind of hindering me. I don't want to be known as an artist who is to do with that artist. I want to be known for my own thing. When my record was coming out people were copy and pasting the [Pitchfork] article like, 'Oh, he thought Frank Ocean didn't like his music'. It was just completely out of context, you know what I mean? And I think it was misquoted as well, so I was like, 'Well fuck this shit. If that's the state of journalism or the state of these music publications then why the fuck do I want to give them an interview?'

I tell Marshall I liked the Pitchfork piece but not so much the way it was teased with a news story about Frank Ocean. "Yeah, it's insulting. Because you've now just covered the story in a completely different light and it's about someone who has way more success than me," he says, half exasperated, half completely disinterested. I follow up with another bit about being a fan and how reading profiles gives listeners extra colour, helping them to learn something. "I guess I learn more myself," he replies, thinking about it. "I done like 60 interviews last week in Europe and by the end of it I had created analysis for almost everything I'd done on the record."

We chat some more – and it's worth noting the exchange is amicable – when I ask whether he finds it helpful to discuss his work with others. "I guess so." Or do you not care? "I don't really care." At one point I say it feels like Marshall does care but it's more to do with holding onto a romanticised, artistic image – one he is in control of. And as if to prove my point, when I return from a toilet break he's sat at the table, journal page open, doodling away. He makes brush strokes with a black pen, saying how he likes to draw outside. When I say what about if it rains, he replies, conversation slowing again, "Maybe it makes the drawing look better. I like wet pages." It's a statement couched in what we know to be true about Marshall: he works to transcend the category of musician and instead earn the title of artist. Frustration is a part of that but in Marshall's work it also comes out as a kind of romance. "I feel like romance is everything. I like the bricks, the way the streets are made," he says. What's the most romantic thing he's done? "I've done a million romantic things, man. That's how I live my life."