Before I meet Dave, rapper, musician, singer, songwriter, award-winner, straight-in-at-Number-Oner, irregular-regular 20-year-old from Streatham, I am allowed to hear his new album. This is a big deal. In fact, it’s such a big deal that Dave’s PR sits in with me when I listen – not to monitor my reaction, but because the album has been kept in such secrecy that he hasn’t heard it yet either. We sit, notebooks out, while a nice woman called Ruby from Dave’s management team plays the 11-track album from her laptop.

Dave’s album is also a big deal because, over the past four years, he’s zoomed from an unknown 16-year-old rap sensation to a platinum-selling artist who, so far, has only released singles (11, not counting special appearances on other people’s), plus two EPs, Six Paths and Game Over. His fans have been clamouring for this LP, bombarding him on social media for over a year.

Although Dave – full name David Orobosa Omoregie – is usually classed as a rapper, he also makes pop, grime and Afrobeats: hits such as No Words (featuring MoStack) showcase not only his gift for a tune, but his decent singing voice; Wanna Know was only out for five weeks before Drake remixed it and added a verse; Funky Friday, with Fredo, beat Calvin Harris and Sam Smith to go straight in at No 1 last year.

But it’s his less poppy, more serious stuff that I like. His words are lyrical and technical, clever and moving, with a melancholic heart that comes not just from the minor chords he plays on the piano. Several of his songs seem almost suffused with pain. Question Time, which directly addresses Theresa May, Jeremy Corbyn and David Cameron, moves through NHS funding, Trump and Grenfell, and won him an Ivor Novello. My 19th Birthday is regretful and complicated: “They tell you that home’s where the heart is, but I got a hole where my heart is.”

There is sunshine, though, as well as shade, sometimes within the same track: last year’s Hangman (my favourite) is beautiful, economic – “between stopping it and living it I’m sitting in the thick of it” – and has a little jazzy outro that actually makes you laugh when you hear it. (In the video for Hangman, Dave’s friends do just this: filming was the first time they’d heard the track, and when the outro is played they start giggling and dancing around.)

Anyway: the album. Entitled Psychodrama, the cover features a blue-tinted painting of Dave with his head in (blue) flames – appropriate imagery for an artist who has so much firing in his brain. Fraser T Smith, veteran of Stormzy and Adele, is a producer; other producers include long-standing collaborator 169 (who’s worked with Headie One, Big Zuu, Jme) and Nana Rogues (Tinie Tempah, Drake).

After we hear it, Ruby, the PR and I, plus the head of the PR company, all hop in a cab to the Observer office for the interview and photoshoot. This morning, Dave has been at designer Ozwald Boateng’s studio, getting fitted for a suit, and we were told he would be late; in fact, he’s already sitting quietly in reception with his friend Justin (Juss), who comes with him everywhere. Dave’s two managers then turn up too. By the time we go into the photo studio, we’re eight-strong. (“More than when we had Kendrick Lamar,” someone says later.) Among this mad throng, Dave himself is low-key, polite, in baseball cap and puffa. He is unfazed by the scruffiness of the photo studio. He has a serious face, a quiet voice. When he smiles, he shows tough metal teeth, but this somehow makes him look even younger. If you give him a compliment, he says “Thank you”, and puts a fist on his heart.

Once everyone has stopped bustling about and left the photography studio, we perch on high seats and talk Psychodrama. Making it, says Dave, took a lot out of him. (He works hard on his songs: he has called them “gold or silver, something rare or precious”.) He started it on 23 January 2018 (the date opens the album), and finished it last month. So, one year. A year when his life was pretty busy – Hangman came out at the beginning, Funky Friday in October, plus he appeared on Avelino’s U Can Stand Up and tried some acting – and he felt changed by the end of it. He hopes the progression is clear: “From the start, when I was more reluctant to speak, to the end, which is embracing the idea that it’s OK to find out a bit about yourself.”

You could call Psychodrama a concept album: the first track is called Psycho, the last Drama, and throughout there is the (acted) voice of a psychotherapist – or “psychodrama-thist”, as Dave says to me – talking to Dave as though he’s in a session, encouraging him to open up about his problems. The album has a three-act structure: act one he defines as “environment”; act two “relationships”; act three “social compass”.

Act one, then. Dave in his environment, as represented by tracks Psycho (“I ain’t psycho, but my life is”), Streatham (self-explanatory) and Black. Black is the first single from the album, and it’s powerful; both angry and celebratory, with some strong lines. “Black is stepping in for your mother because your father’s gone… You don’t know the truth about your race cos they erasing it… Representing countries that never even existed while your grandmother was living.” (Some Radio 1 listeners have complained about Black’s “negativity”; DJs Annie Mac and Greg James took them to task.) Dave recorded it towards the end of the album process: he’d meant to make an upbeat tune, but instead he wrote a darker instrumental (he usually works on the music before the lyrics: it sets his mood). The words took him some time, as he did a lot of research, including talking with a Ghanaian friend who’d been tracing his family tree (the friend discovered that he was, in fact, Egyptian).

“That track is my experience,” says Dave. “Me being south London, black, Nigerian, that’s what I’m mainly basing it on. It’s a good representation of what I associate with and everything that I think, but I don’t think that it’s universal for the whole black experience, because there’s too many different races and dynamics within the race of black. For a black person who’s Senegalese, growing up in France, or a New York Jamaican, that’s a completely different relationship with being black and how you might be accepted in that culture or that world. Everyone’s experience is different. Especially black women and black men.”

Despite his research, even now, he isn’t sure. “Black is confusing. Where does the line start and stop with what is black and what isn’t black?” He feels as though society lumps all black people together, and he wonders how carefully people are looking. “People that are mixed-race, or, imagine being from Sri Lanka or Bangladesh, people might say you’re black but your features are so non-black, like you’ve got straight hair, you’ve got like a sharper nose, or such. No matter what people can see, whether black African, black Jamaican, black British, black American people… they just say it’s one thing.”

Back to the album. Act two, the middle section, is catchy and poppy. Act three is interesting, with a couple of tracks that call back to Streatham, but with more insight: “You see a gangster, I see insecurity.” There’s an 11-minute track called Lesley that’s like a movie in song form: “A story about someone suffering a complete loss of character by being with someone that isn’t good for them,” says Dave. And then Voices, the penultimate track, which I assumed was about a relationship – “I fell in love with optimism” – is, it turns out, about Dave himself. “That whole track is metaphorical,” he says, “but it’s about a constant chase for happiness. So when I’m saying, ‘All my life, I hear voices when I sleep, and they say, “You’re everything I need”,’ the everything I need is myself. Inner happiness. What everyone’s looking for.”

Drama, the final track, sits slightly separately from the others. It features a recording of a phone call from Chris, the younger of Dave’s two older brothers, who’s in prison serving a life sentence. “The concept of psychodrama actually came from the type of therapy Chris has been having in prison,” says Dave. “The whole idea for the album, everything’s based off him, and that song is a conversation between me and him.” In the track, Dave uses Chris’s words to create lyrics. Chris mentions living on the edge, like a house on a cliff, which Dave runs with; and “forget the other brother that was even bigger, we were figures just trying to figure out if we could be a figure” – he says that’s Chris’s too.

The lyrics that stuck with me, I say, are “I don’t have a vision of a marriage or a wedding ring, world domination in music or it ain’t anything. Obsessed.” And “I learned all the time the separation issues I described are probably the reason that I struggled feeling anything.”

“Well,” he says, “those are the truth.”

Photograph: Phil Fisk/The Observer

Though they are close now, when they were growing up, Dave and his brothers weren’t, particularly. Ben was eight years older than Dave, Chris five, so they were always at different stages in their lives: one at college, one at secondary school, one in primary. Their dad wasn’t around to bring them closer – “I didn’t get a chance to have any memories with him” – and their mum often worked day and evenings, as a nurse and cleaner, to support her family.

Dave was academic and quite serious as a kid, and when I ask him about childish things – hobbies, posters on the wall – he simply can’t answer me. “I wouldn’t have thought to go and get a poster,” he says. “I just sort of existed. I was in this long trance of just waking up, going to school, coming back. I never really had a crazy outward personality, I only found that when I was 15, 16.”

Actually, his mum decided not to let Dave out after school from the age of 11. That was when Chris was sent to prison (he was involved in the killing of Sofyen Belamouadden), followed by Ben, for robbery, a few years later. Dave’s mum reacted by keeping her youngest son at home as much as she could. (Chris agreed; he would phone Dave to check.) It was hard for the young Dave, and not just because he didn’t go out socially. He would visit his brothers in prison – they were moved all over the place – and absorb his mum’s trauma. “I don’t know how she felt,” he says, now. “Too many different things.” He grew up quickly, though he feels that would have happened anyway, just living in London.

“It’s not the same as having a friend in prison,” he says. “Where it’s my brother, the impact that it has on my mum, on the rest of us, the impact it has on anything good… I never want to sound like I’m speaking about prison and I’m crying or moping. But it was definitely a massive knock-on effect for all of us. It’s been a tough journey for everyone involved.”

Trapped indoors as he was, young Dave tried a bit of rapping, putting out a track when he was 13. (“Everyone hated it,” he laughs. “So I retired. From 13 to 15, that was my retirement.”) Then, when he was 14, his mum got him a digital keyboard, and he decided to learn how to play. He liked film soundtracks, the tunes from anime, and he fancied trying to make music. So he challenged his friend Kyle to learn piano with him. Each week, they would each choose a piece – Leonard Cohen’s Hallelujah, or a song from an anime show – and then track down the sheet music online, learn it, practise it and compete with each other as to who played the best song. Dave was playing piano for four or five hours every night, encouraged by his music teacher at school. (He’s still close to Kyle, and Kyle plays on Psychodrama.)

When he was 16, on the first day he went to sixth-form college in Richmond (to study philosophy, ethics, law and sound design), Dave released a freestyle on rap station Bl@ckbox. Within months he was on Jamal Edwards’s influential SBTV; a year later, sampled by Drake. His life changed.

Last summer, when Ben came out of prison after four years, Dave was able to give him money; he’d had nothing when Ben went in. Now, he’s planning to buy a new house, for him and his mum. “I was always going to move with my mum,” he says. “It was always going to happen.” He wants her to give up work, but she won’t. Not until she’s 60 (she’s 55 now).

Prison hosts a lot of normal people, a lot of family men who were caught in a tight situation or in a dark place

There is a lot going on. Dave’s been trying his hand at acting, which he enjoyed, though he found it hard to adjust to at first. “I hated the lack of flexibility,” he says. “They pick you up 5am, and you got to be there, you got to do makeup, got to do costume. If you’re late, there’s people that you answer to. It’s like being at school again. And other things, like getting used to the fact that you’re actually a very small part of a big moving picture. Or, like, I spent my whole life looking into the lens of a camera. And then to be told you can’t look at the lens.”

He’s been getting wound up about football. He supports Manchester United, because his brothers had already taken Chelsea and Arsenal, and got some stick online over United’s recent match against Paris Saint-Germain, as he’d made a track with AJ Tracey about Thiago Silva, a PSG player. “I’m actually connected to football way harder than people think. So I get really rattled, and I have to come off Twitter.”

As you might guess from his track Question Time, Dave is interested in politics. He’s funny and engaged on Brexit (he voted Remain, because of the European Court of Human Rights). He has friends who voted Leave – “Kyle did! Wasteman!” – but he understands why. “Everyone pretends,” he says. “You might say, ‘This is what is best for the country,’ but it’s not ever about what’s best for the country. It’s what’s best for you inside of the country.” He sees this in domestic politics, too. “You might say, ‘I’m going to vote for Labour because they going to make the public sector a lot more funded and blah-blah-blah.’ Really, it’s going to make your life easier. But if you’re making tens of millions a year, you know that if someone from Labour gets voted in, you might be getting super taxed, so you support the other group.”

And perhaps unsurprisingly, he’s been considering prison reform.

“When you strip it back,” he says, “we’re all just humans at the end of the day. Where wrong is done, wrong needs to be punished, but there’s a lot of things that I see. Prison hosts a lot of normal people, a lot of family men who were caught in a tight situation or in a dark place. I don’t think that one moment in people’s life should define them. Within reason: I emphasise that. It’s difficult, because it’s on a case-by-case basis and some people don’t want to hear about reform with certain crimes. But people that are in those positions [in prison] need an incentive for reform, and sometimes necessary support to go out and better themselves and be more functional members of society. If everyone’s on the same page, that is the end goal for people that do wrong, isn’t it? For them to come out and not do wrong again.”

When he was younger, and getting into the odd bit of trouble, Dave had a few therapy sessions himself. He understood why, but, as he gets older, he thinks that therapy “isn’t necessarily always in the form of someone sitting down with a notepad. It might be a friend who you call in the night.” He used to beat himself up about stuff, or want to speak about it online, but he’s a little easier on himself now. He’s cutting down on the internet chat, on explaining himself for video platforms. He’s clear in his lyrics, he thinks. I agree: Dave’s words are a thing of beauty. His art explains his life, sometimes in a way he can’t completely understand.

“Sometimes I sit down and I think ‘Do I regret this? Do I regret that?’ And I feel like everything makes this snowball effect, you know? If you regret something, it’s good because it just means that it’s something that’s affected you enough for you to stop and think... There’s a reason that everything happens.”

He quotes a lyric to me, from another rapper, about the Garden of Eden. He loves this lyric. “Because everything wouldn’t be everything,” says Dave, “if the Garden of Eden went right.”

Psychodrama is released on Friday on Neighbourhood. Psychodrama: the tour starts in Dublin on 9 April and ends in London on 3 May