"This is where it all happens," says the star, who has scored more number one singles (seven) than any other British artist this decade, as he welcomes the BBC to his studio.
It's a pristine room, free of clutter and distractions, except for a PlayStation 4 and several years' worth of Fifa games.
On the mixing desk sits a book on Frank Gehry's architecture, while the far corner is dominated by a gargantuan bean bag, apparently fashioned from the skin of a dead muppet.
Outside the sliding glass doors, Tinie has a child-sized Lamborghini, which he's planning to use in an upcoming video.
"Jake Bugg has been here," he says. "MNEK's been here. Sinead Harnett was here the other day.
"Lewis Hamilton came here not long ago - but not to do a guest vocal."
The studio has been Tinie's second home since 2008. He recorded his million-selling debut Disc-Overy here. And it's where he's been obsessing over his third album, Youth, for more than two years.
The record has suffered a number of delays as the star revised and refined the tracklist. Part of the problem was that, after five years of success, he'd lost touch with his roots.
"I've been on the road literally since I released Pass Out," he says. "I've been in my own world and my own head.
"My engineer Ritchie said, 'You know how you'd be able to nail this album? Move back into your mum's house. Take all your stuff and live your life from there.'
"But obviously you can't do that. It would just be too annoying. So what I did instead was make sure I met up with all my friends and did the things I did before this all happened.
"That was the creativity behind the album, catching up with my friends."
You can hear it in the music. There's a playfulness and warmth that was missing from Tinie's second album Demonstration, which found the rapper struggling to come to terms with fame. He symbolically scratched his eyes out on the cover, fearing he'd become too much of a "personality".
On Youth, he steps back and counts his blessings.
"It was such a strange thing to be a British rapper when I started," he says. "People were like, 'Oh, you're rapping with an English accent? Naaaah.'
"Now that's changed. Look at the likes of Stormzy and Dave - there's a plethora of British rappers. It's an accepted genre now. It means something to British culture on a mainstream level."
Tinie was born Patrick Chukwuemeka Okogwu Jr, and spent his early years in Peckham's notoriously rough Aylesbury estate.
But by the time he was 12, his father, a barber turned social worker, and mother, an NHS administrator, had saved up enough money to move the family to the quiet, leafy suburbs of Plumstead.
Patrick picked up his parents' work ethic, gaining A-Levels in media studies, religious studies and psychology - but was seduced by music after seeing So Solid Crew on TV.
Rap, he suddenly realised, didn't have to come from the other side of the Atlantic.
He took a job selling double glazing to fund his early recordings, and emerged as part of the grime scene with tracks like Wifey and Tears.
Soon he was developing his own sound - a futuristic mix of hip-hop, synth-pop and space-age dub, laced with a wry awareness of rap cliche.
"I got so many clothes I keep 'em in my aunt's house," he quipped on his breakout hit Pass Out.
He acknowledges his musical progression on a new song called Not for the Radio. "Eight years sitting on top/Hip-hop, grime, then I went pop."
Yet for all his chart-busting collaborations with pop stars like Ellie Goulding and Jess Glynne, he hasn't forgotten his roots. "I listen to grime still, I go to events, I partake in the music," he says.
What impresses him most about the new generation of artists is their self-reliance - in particular Skepta and Stormzy, who've hit the big time while recording and releasing songs on their own labels.
"Against all the odds, they're setting up their own infrastructure, putting out records, creating their own hype and achieving things that, five years ago, you could only have achieved on a major label," marvels the rapper.
Tinie also retains the rights to his music, while licensing it to Warner Music subsidiary Parlophone.
Grime's success is particularly encouraging because, he says, it "was almost like the uninvited genre".
He says: "People have likened it to punk but I feel like, for some reason, it wasn't embraced. It got pushed to the side.
"I think that's basically changed now. We get to be ourselves and make hits, just like everybody else."
He addresses the genre's success on another album track, Lightwork: "Black boys getting white paper/From the underground, now we're in the skyscraper."
Reconnecting with friends while making Youth, Tinie realised that obsessing over his career had robbed him of other experiences. But it's a price he says was worth paying.
"A lot of my mates from school are married, some of them have got kids, some of them have got two or three," he reflects.
"It's weird: I can be sitting with a friend, telling them about all the amazing things I've seen on tour. Like, 'I played in the Maldives in an underwater club!' Or, 'I did the Olympics!' And they'll be sitting there thinking, 'Wow, I'd love to do what you're doing.'
"But equally, they can tell you, 'Mate, I just got married. You missed the wedding. And now my wife is expecting her first child.' And I'll be like, 'Wow, you're getting on with your life and it seems like you're really happy.'
"But I don't feel I'm missing out. If you ask any musician who's operating at a certain level, you swear your life to your art, if that makes sense.
"So I don't want to upset anyone that's reading this - but it's almost like the art comes before pretty much everything else."
Tinie Tempah's album Youth is out on 14 April.
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In a nondescript apartment complex half a mile from the Cutty Sark, Tinie Tempah conjures up some of the biggest hits in UK hip-hop.