Anarchy in the UK: Aussie comic Tim Minchin is fomenting childish revolt after getting his hands on Roald Dahl

Look at my eyes." Tim Minchin has not been sleeping well – and with good reason. The Aussie musical comic has been a busy boy recently, preparing for the consecutive opening nights of both his new musical for the Royal Shakespeare Company, based on Roald Dahl's Matilda, and a UK arena stand-up tour in cahoots with a 55-piece orchestra. "I've been insanely stressed," he says. "I have to go to bed shattered or my heart just goes whoom."

Going to bed shattered presumably isn't hard to achieve – today, or at any time over the past five years. In 2005, Minchin brought his piano-and-jokes shtick to the Edinburgh Fringe for the first time, and secured the Perrier Award for Best Newcomer. His subsequent rise has been both spectacular and stealthy. Without the usual TV overexposure, and despite being billed the "Richard Dawkins of comedy" for his rationalist subject matter, the 35-year-old has established himself as our favourite adopted rock-star comic.

I can't better Minchin's own explanation of his success, which – in its matter-of-factness about his own powers – is typical of the man. "If you're a jazz or classical connoisseur, you can go any night of the week and see a musician 10 times better than me, and have your mind blown. But most people never see someone really playing an instrument; really going at it hard and enjoying their craft." Make that crafts, plural. Minchin's wordplay is as dexterous as his ivory-whacking fingers.

His success is easily explicable, then – but it was also wholly accidental. Throughout his twenties in Perth, Australia, Minchin was a jobbing actor and writer, supplying tunes for local theatres and playing keyboards in a covers band. The comedy career snuck up on him, when audiences at the 2003 Melbourne Festival found his debut cabaret show funnier than he expected. Yet the transformation was, and remains, tentative. Minchin's shows feature non-comic songs alongside the funnies. His most famous number, a nine-minute Beat poem called "Storm", in which Minchin tears into a credulous New Ager at a dinner party, is as serious as it is funny. He includes anti-superstition material in each of his shows "not because I'm trying to educate people, but because most of what I think about is how beautiful nature is, and how wacky it is that people believe shit that doesn't seem to be the case".

Then there's Matilda, on which Minchin has been working for a year. First contact with the RSC, which invited him to add music and lyrics to playwright Dennis Kelly's book, was a transformative moment for him. Not least because of the serendipity: 10 years previously, he had applied to the Dahl estate for stage rights to that very novel. "Like nearly everyone," he says, "Dahl is embedded in my sense of child-ness. As soon as I encountered Matilda, I was struck by [the feeling of] how is that not a musical yet?"

The Minchin-Matilda connection is simple to discern. She is the abused child genius who wreaks revenge on the adult world. He, kohl-eyed and shock-haired, plays the delinquent child in his stand-up – before sitting at the piano and proving himself a prodigy. The quality in his new musical that most excites Minchin is its "promotion of anarchy. The thesis Dahl visits again and again is that children, if they use their childishness, their mischief and ingenuity, if they don't sit in front of tellies but read books and be adventurous, can overwhelm their grown-up oppressors."

His excitement about the project extends beyond his belief that he's made a great show. It relates to the fact that he's found himself again. "Writing music-theatre is what I started doing when I was 17," he says. "I was never a good pop musician, as I write theatrically: dense lyrics that tell stories and music that dabbles in all sorts of styles. I've re-found my thing, but now with a load of confidence as I have a successful career, so I don't have to hate myself every morning. And it's the RSC who asked me to do it, so I can't be a total chump."

Does that mean comedy was an aberration? Not exactly. Minchin has a vexed relationship with stand-up. "There's something dirty and sleeping-with-a-hooker about comedy," he says. "It's an artistic one-night stand. Once you've heard it, it's spoilt. Once you've had it, it's dirty." By contrast, he describes in awestruck tones how, halfway through creating Matilda, Dennis Kelly axed a character for whom Minchin had written his two best songs. Minchin was distraught – "it took me three months to get over it" – but now hymns the episode as an example of the cut-and-thrust rigour of artistic collaboration that solo stand-up denies him.

He is also wary of the narcissism of stand-up – because "I've got that in me," he admits. As if we needed telling. One of his songs, which names and crucifies a reviewer who one-starred Minchin's Edinburgh debut, is the last word in thin-skinned aversion to criticism. Minchin's capacity for introspection and obsessiveness is likewise easy to detect. He is breezy and friendly in interview, but now and then worries at a question like a dog with a bone. Repeatedly, he tells me what will and won't read well in this article. After the tape has been switched off, he regales me and his PR with lyrics from his new songs.

But he is still committed to comedy – albeit as one activity among many, which will one day include acting, he hopes, "and writing straight plays, if I can. And recording albums of non-funny songs." His comedy can be collaborative, too, as Minchin hopes to prove with his orchestra tour. The plan was to bring that show from Australia, where it originated, to the UK in lieu of the new stand-up set that Matilda has prevented him writing. But Minchin ended up writing a "two-thirds' new" show anyway. "I didn't want just to take a show from a smaller venue and put it in a big venue. I wanted a show that couldn't be anywhere but an arena." And besides, "I saw Muse at Wembley Stadium and I thought, I have to make it even more stupid than that."

Several recent comedy events – Monty Python's reunion at the Albert Hall, Barry Humphries' Last Night of the Poms – have twinned orchestras and comedy to lumbering effect. Is Minchin worried his new backing band will clip his wings? "You can't just staple them on," he admits, "because all they'll do is make your songs sound more like songs and less like comedy. An orchestra is funniest when it's doing massive classical turns in the service of stupid ideas." He tells me with joy that the whole orchestra will sing "motherfucker" in his song about the Pope. Elsewhere, the show sends up what Minchin calls the "paradox" of arena comedy: "This idea that you're so big that you don't have to give people a good experience any more. My first song is about that, which obliges me to ensure that I'm the exception to the rule."

Hence the sleepless nights. "It's ridiculous that I have a musical at the RSC and an arena tour opening on consecutive nights," he says. He takes refuge, of course, in rationalism. "I keep telling myself that my stress isn't about logistics, it's just me coming to terms with the idea. And that shouldn't stress you, because it's just conceptual. If you can't get your head around it, don't. Just make the songs as good as you can, and when you walk out on stage, you either cope or you don't. And what I do know is, I'll cope," he says, relieved at the thought. "I'll probably be fine."

'Matilda' is previewing now at the RSC's Courtyard Theatre, Stratford (tel: 0844 800 1110). Tim Minchin and his Orchestra play Brighton tomorrow (tel: 0844 847 1515). For full details of the tour, visit timminchin.com

Musical leanings: Tim's top five shows

Jesus Christ Superstar

"I've loved this since I was a kid. In the original production, they had 30 members of the LSO in the pit, with the drummer, guitarist and bassist from Deep Purple, and a couple of guys from Motörhead. And on stage, Ian Gillan from Deep Purple playing Jesus. That's brilliant. And it's a genuinely atheist musical! It's so cool."

Starlight Express

"It changed my life. I saw it in London when I was 10, and there was a ramp that went behind me, it was loud and I knew all the songs. That power to blow your mind is what you want to remember."

Oliver

"Oliver is brilliant. As a kid I had a pianola that was my grandmother's and we used to sit around and sing all these songs. Most of the musicals I know, I know because we had a pianola roll of it."

Gilbert and Sullivan

"There was a Gilbert and Sullivan society in Perth, which I thought was the peak of theatrical production. Somewhere I got the joy of playing with words and making them rhyme, and I didn't listen to Tom Lehrer."

A Little Night Music

"Sondheim is incredible. Someone lesser writing a musical might write 'What fools are we'. But he writes 'Send in the clowns'. That's worth its weight in gold."