It's 9.02am on Friday and I am being given a refresher course in live radio DJing by 6Music breakfast show host Shaun Keaveny.

"When I say, 'Now,'" says Shaun, "press that button there. That red one." His producer, Lisa Kenlock, looks at us over the top of her computer screen. She is smiling, but her eyes are grave. Phil Smith, the other producer, and Matt Everitt, who does the music news, are also watching. Ooh, the pressure. "Now!" says Shaun. I press the button and M83's "Reunion" segues into a 6Music trail. Everyone cheers. I curtsy and sit down. My work here is done.

This small stunt has come about because BBC Radio 6Music will turn 10 years old on 5 March. Happy birthday, the 6! Home of credible alternative music, of clever, off-beat, older presenters, 6 Music enters its second decade with its confidence and its listenership high – around 1.2 million regulars, tuning in for longer hours than ever before. But such upbeat days were born of tricky times; today's easy-on-the-ear listen disguises the work behind the scenes. And so my job this morning is to observe how difficult live DJing is by watching Keaveny at work.

Unfortunately, he makes everything look easy, biffing banter at Matt, picking up a guitar for an impromptu rendition of "Wonderful Tonight", interviewing a sleepy Brian Cox on the phone, composing two-line poems for Middle Age Shout Outs – all in between pressing the right buttons at the right times. Middle Age Shout Outs is a regular Friday morning item: listeners get in touch to say what they're up to at the weekend and Shaun turns this into a dancehall-style rhyme. One listener informs that he's going to buy a Henry hoover. "Hoover with eyes/ It's a pet surprise," raps Shaun. "Cos they always scare dogs, don't they, those hoovers?"

Shaun has been on 6 since 2007 and in that time his show, and the station itself, has been through fundamental identity crises. Brought over from Xfm by then-controller Lesley Douglas, Keaveny spent his first year on Breakfast in a thorough-going funk. In those days, his show was followed by another Douglas protege, George Lamb, a talented broadcaster whose mickey-taking, urban geezer attitude was all wrong for the station – but got a lot of attention. Lamb played mad ragga tunes and shouted: "Shabba!" Shaun seethed and carefully wrote jokes into his script.

"Actually, I learnt a lot from George," he says now. "Things about having more of a relationship with people you work with and with the listeners. I was brought up on overnights at Xfm where I was by myself. I didn't have anyone to bounce off, so I used to script my links. I slowly learned to relax and create an environment where you can be spontaneous by including other people."

That inclusiveness, that sense of understanding between presenters, producers and audience is now part of 6's DNA, as it is with all brilliant radio stations. But for 6, it came about through a series of calamities. So let's go back to the start.

Andrew Collins, who had the teatime show when 6Music began, and who still presents shows for the station, recalls the reason why the station is here at all. "It was a canary-down-the-mineshaft thing," he says. "The BBC, to its credit, thought the best way to publicise digital services was to create some digital stations. The Asian Network, 1Xtra, Radio 7 and 6Music came out of that."

Then, the station felt anarchic, almost unknown, anonymous enough at least to be able to do what it wanted. Its producers were young and learning; its DJs were older, but still working out what to do, what 6 was for. Supposedly, it was a bridge between Radios 1 and 2, but it never felt like that. It felt more muso, more chin-scratchy, silly and sincere. And it was small. I was a stand-in presenter for a couple of shows and I thought I'd rely on listeners' emails for a sense of what to talk about. But only a handful of regulars got in touch (though those who did did a lot). 6 really was a niche concern.

The BBC was never going to let 6Music continue in its haphazard, stuff-the-audience-figures way. Douglas brought in Keaveny and Lamb to increase ratings and, supposedly, to appeal to women – but then had to resign, when another of her proteges, Russell Brand, brought the radio world crashing down with Sachsgate. Bob Shennan became 6's controller. Though there were initial mutterings about his lack of music background (his longest previous stint was at 5 Live), Shennan has proved astute. His first move – to replace George Lamb with Lauren Laverne in 2009 – was inspired and he's gradually tweaked the station, pruning the cutting-edge dance elements, growing the musician-turned-presenter pool (it now boasts Jarvis Cocker, Cerys Matthews, Guy Garvey and Huey Morgan among its roster), shaping it into the cool, sure-footed offering it is today.

It was in 2010, though, that 6Music really faced disaster. The BBC, asked to make massive savings by the government, proposed closing the station altogether. Or, if not, then turning it into Radio 2 Extra, broadcasting during the day and joining up with 2's output in the evenings. It was a genuine threat and the reaction of listeners was huge. They marched on Broadcasting House, they sent petitions to Parliament, they marshalled support on Twitter and Facebook… And they won. The BBC Trust concluded that the station must continue. And the trust's codicil – that 6 must employ more DJs who knew their music – was even more of a validation.

The boost to the station was immense. Not only did the protest serve as a publicity campaign, doubling 6's audience in a matter of weeks, but it gave the whole place a status, an "approved by" legitimacy. "The station being threatened, and then saved, changed everything," remembers Shaun. "It brought the best out of everyone and made us realise how culturally significant 6Music is. We knew we were part of something that everyone believed in."

This new confidence made Shennan's subsequent high-profile hirings – stars such as Jarvis Cocker, veterans such as Mark Radcliffe and Stuart Maconie – seem natural. Now 6Music feels, if not like a cringe-worthy family a la Radio 1, like a bunch of people who understand one another. A collective that gets it, that represents a small, but significant, segment of Britain's population.

"It's not like we're all going out in central London getting drunk together," says Keaveny of the 6Music team. "We're all quite old. We've got lives, families, some people are up in Manchester. But we've all got respect for what everybody does. We've all got the same attitude to life. And so have the listeners. Some people get to their 40s and become entrenched, start reading the Daily Mail and listening to Magic FM. But if you've still got a restless intellect, you're still excited by life, you're still reading books, you're perhaps a person who's started a record-playing evening at your local pub… that's what everyone's like at 6. That's why we all get on."