DJ Geeneus is remembering the first ever Rinse FM radio broadcast, as a pirate station, in September 1994. "One of my friends got their first flat, so we were like, Great, we'll stick the studio in the kitchen, 'cause you're not going to be using your kitchen that much… We was 18 floors up and we put the aerial out the balcony window, moved it around… And then the front door come flying off and some old geezer come flying in, screaming at us, going, 'My telly!' He was watching the rugby and he could hear our radio station coming through his telly!"

This and other torrid tales of pirate radio – of mad dogs and policemen, of grime MCs and dubstep DJs, of asbos stopping people from going above the fourth floor on any tower block, of the slow progress from criminal outsider to we're-not-leaving legality – can be found on Rinse FM's website. There are 18 video clips, marching through the station's history. They include household names such as Ms Dynamite and Katy B, and they make an exhilarating, inspiring watch.

I'm watching Geeneus's clip in Rinse FM's offices, in the Truman Brewery complex on Brick Lane, east London. This is slightly awkward, because Geeneus himself – real name Gordon Warren, 34 – has just come in. Neat, wary, inscrutable behind big shades, he quickly reveals himself to be an expressive talker and offbeat thinker. He started Rinse, with DJ Slimzee and a few others, when he was just 16.

"Does it seem a long time ago?" he says. "I dunno, I don't really think about time like that. I wake up and go to sleep and do what I'm doing in between. I believe you're born and then you die; I don't believe in birthdays."

Not a man for a cake and candles, then; still, this weekend saw big Rinse parties in Manchester and London because the station – give it the bumps! – just turned 18. Thousands of punters turned up to party to the likes of Boy Better Know, Kode9, Skream, Diplo and Modeselektor. Many others will have tuned in via FM or the internet. Not you? Well, it's fair to say that, even if you've never listened to Rinse, you'll have heard its legacy: MCs turned pop stars Dizzee Rascal and Wiley; grime, dubstep, funky; the distinctively UK dance sound that's dominated the pop charts for the past few years – all have had Rinse involved at some point in their story.

But there have been – there are – umpteen pirate radio stations. Why has Rinse succeeded? How did a group of music-mad school leavers, hanging an aerial out of a tower block window, end up here: slick offices on two floors, containing a broadcasting studio that wouldn't be out of place at Radio 1, a successful label, an artist management team, 12 employees. Today, around the central trio of Rinse, the radio station, Tempa, the record label, and FWD>> (Forward), the underground club, there are a myriad creative ideas taking root. Such as the Rinse Academy, which takes young people with musical or broadcasting promise, helps them hone their craft and make the right business connections to succeed. Or the curated evening at Tate Modern's new Tanks space which the team hosted over the summer (they took 10 important tracks that went from underground to overground, and mixed them with lights and performance to create an art-rave). Not forgetting that, as of 2010, Rinse has been legal, with its own space on the FM dial: 106.8FM. That noisy baby has become a successful, legitimate adult. David Cameron, were he ever to look further than the Bullingdon Club for his "big society" successes, might be pleasurably surprised.

Rinse FM's legal status was hard won: it took "Gee"'s business partner, Sarah Lockhart, who started FWD>>, five years of unbelievably hard slog to get the licence. From the moment she joined Rinse in 2005, it was all she was focused on. She describes it as like studying for a degree. She had Post-Its and numbers and arrows all over one wall, as though she was part of a police team searching for a serial killer. Still Sarah, like Gee, is a force to be reckoned with: singular and single-minded.

"I never thought we wouldn't do it," she says. "Me and Gee are the same. We've always been disregarded, we get told that what we're doing won't work in the real world. And we're like, Oh really? And we just carry on and eventually surprise people."

We've moved into a small room off the studio, where breakfast show host Tinea Taylor is doing her thing; just her and one producer, as far as I can see. In this space, empty except for some computers, Gee perches on a bench, Sarah diagonally opposite. Next to me is Katy B, singer, Mercury nominee, pop star. Properly stunning in photo makeup and sparkly top, she's part of the Rinse family; her debut album, On a Mission, was the result of collaborations with Gee, and Rinse DJs Zinc and Benga.

Katy met Gee when she was 16 at a club in Barking, where he was DJing. "He says I stole his Haribo," she laughs, "but I don't remember that."

She started working with Geeneus, on and off, until Rinse asked her to provide vocals for an album, intended to showcase the station's DJs. Each DJ was to do one tune, with Katy singing across all the tracks. It morphed into her debut LP.

"I always think of Katy B as a band," she says. "There's me and Geeneus, and it was Rinse's idea. I had the drive for music, but it wasn't the internet or YouTube that broke it for me. Rinse gave me the break."

Katy's working on her second album now, and looks to Gee when I ask how it's progressing. "It'll be done by the end of the year," he reckons. "We'll work right up till the last day, because sometimes it's on the last day that you come up with a track." Katy tells me that this album will be more romantic than her debut – On a Mission had its share of love songs but was, essentially, about Katy's romance with nightclubs and music – and then she's off, to make it.

After she's left, Gee, Sarah and I talk about Rinse becoming legal. For Rinse to get a broadcasting licence was a massive deal. Very, very few pirate stations manage it, the most high profile being the original Kiss FM, way back in 1990. Most pirates, even the long established, such as Kool(two years older than Rinse), just don't bother. It's too much hassle. Many, these days, simply stick with streaming over the net, and don't bother with FM at all. The establishment – the DTI, Ofcom – has an establishment line: there are no FM frequencies available. And when any come up, it's not pirates that they want to apply. As far as regulators are concerned, pirates are a pain. Their broadcasts can bleed into frequencies used for emergency services or, even worse, fuzz up Radio 4; they're often run by people connected with drugs and violence; they use bad language during school hours; they play too loud.

The cleverer pirates know this and don't break those rules. But they're still a DTI raid away from being taken off air. For Rinse, the illegal nature of being a pirate began to hold the station back: it wanted to work with the police, running an anti-violence campaign targeting local kids, but it couldn't. It was running legitimate businesses with the label and its clubs, and wanted to expand – but the station, the centre of it all, was illegal. "It meant people could dismiss us," says Sarah.

So she persevered. And in the end, Rinse applied – and got – a community broadcasting licence. The distinction means nothing to listeners, but quite a lot to the application. Usually, community stations are small, broadcasting just a few miles around their transmitters, so five stations can be squeezed on to one frequency. Rinse applied for the whole frequency, and made the argument that its community wasn't just what Sarah calls "Shoreditch FM" but a community of young people interested in a certain kind of music.

And when Rinse got the licence, it changed everything and nothing. It arrived when, says Sarah, "everything we'd been working on suddenly came together". Katy B's album came out; dubstep, which Rinse and FWD>> had championed, went big; grime MCs such as Tinchy Stryder and Tinie Tempah became mainstream. The licence just turned out to be a piece of paper on the office wall. Rinse carried on as before. "We're like that fish in Finding Nemo that goes, Just keep swimming, just keep swimming…"

While it's keeping on keeping on, there are a few Rinse golden rules. The first is the search for brilliant new music. Gee and Sarah and everyone they work with are obsessed with tunes and aren't afraid to promote stuff that no one else is playing. In fact, another Rinse rule is what they call "destroy and rebuild". When a genre of music goes big, Rinse moves on. When grime and its MCs dominated the station, in the mid 00s, Gee took the decision to take Rinse off air for a few months. When the station came back, it played dubstep: slower, bassier, instrumental, without an MC within spitting distance. Similarly, Sarah kept moving FWD>> around, shutting it down, changing it to a Sunday, between 6pm and midnight, just to keep it special and for the proper music heads.

For Gee and Sarah, it's important for Rinse to be legitimate, but not mainstream. It's looking for some big-name sponsors for the Rinse Academy, but it's not turning it into the Brit School. It would like to do more video work, but only if it can involve brands that understand what Rinse is about. Its DJs still do shout-outs, as opposed to carefully reading out emails; it hosts nights for just a few hundred anoraks; it asks DJs to move on once they've got too big, to make room for the younger, hungrier, new generation.

"When you're 17, 18, you're full of yourself," says Sarah. "And that's brilliant. We get people here just hanging around, and they're great, just nutcases, big personalities. They're creative, but no one's recognised it."

"Everyone's got ability, but places like school just shut it down," says Gee. "We let people let it out. We're like a job centre, but a good one."