When Tim Minchin played to adoring, sell-out crowds on the steps of the Sydney Opera House Forecourt in February, he included a song called Seeing You, from Groundhog Day, the new musical he is currently working on.

He has also performed the song at London’s Hyde Park and various other gigs. As a first-taste introduction to Groundhog Day, the gentle, lilting, country ballad is excitingly promising.

“It’s a bit weird because it’s the final song in the whole musical so it doesn’t really give you the tone of what’s gone on before,” says Minchin.

Groundhog Day follows in the wake of the phenomenal success of the Royal Shakespeare Company production of Matilda the Musical for which Minchin wrote music and lyrics.

It’s based on the brilliant 1993 film: a comedy classic scripted by Danny Rubin and starring Bill Murray and Andie MacDowell. Rubin himself is writing the book, Minchin is writing music and lyrics, and Matthew Warchus, who helmed Matilda, is directing.

The show will premiere at London’s Old Vic next year as part of Warchus’s inaugural season as artistic director, prior to a Broadway opening in 2017.

Writing on his blog, when news of the project leaked last year, Minchin described the plot in his inimitable way: “For the handful of you who’ve never seen the film (philistines!), Groundhog Day is about a cantankerous weatherman who is sent to a small town to do a weather report, and gets stuck in a time loop, living the same day over and over again until – eventually – he figures out how to be less of a miserable, egotistical git. It’s about selflessness and acceptance and love and time and life and death and all that good stuff.”

Minchin says that their stage adaptation will be “instantly recognisable and utterly different”.

“The narrative is very similar but tonally it’s completely different. You can’t make the character of Phil like Bill Murray – by which I mean the Bill Murray-ness of that character would not allow him to sing. It can’t be Bill Murray. It has to be a slightly more standard Scroogian character,” he says.

“And also you can’t write a piece of theatre – or I don’t want to in 2015 – with a woman as passive as Andie MacDowell. You take the opportunity to write a stronger woman whose influence is more profound and who has her own sense of humour. Andie was very charming in that movie but we need to know more about her.

“In musicals – just like in Matilda – you want to know more. You can’t maintain a distance in a musical and that’s why you have to consider very seriously which texts you do. Is going into their head – which is what a musical does because they sing their feelings – is going into their head going to help us?

“And if you are going into their head, how do you make sure the character doesn’t become mawkish and over demonstrative? That’s the problem with Matilda and Miss Honey (in Matilda). Miss Honey isn’t a demonstrative person so how do you get her to sing? That’s why I made her sing about her house, which is her singing about herself by not singing about herself. Those sorts of solutions are what musical theatre writers have always done but Groundhog Day is a particular challenge like that because you’ve got to keep it funny and witty and dry.”

In the story, the same scenes keep playing out, with the weatherman Phil gradually responding differently each time he relives a moment. Asked whether the music will repeat with gradual transformations, Minchin says not.

“Music reflects your protagonist’s state of mind. You could take the same music and put different angles on it but I realised early on that it’s not the songs repeating – because songs repeating is not unconventional. It’s dialogue and action repeating which is where the magic is in theatre. You have a complex series of events that are exactly the same. That’s like a magic trick; that’s awesome.”

Minchin says the songs will have a more poppy feel than Matilda. “It’s less Dahly. There are songs you could play on the radio. Anyway, it’s such an exciting challenge. I just hope we don’t fuck it up.”

Minchin is currently alternating between writing the songs for Groundhog Day and the songs for Larrikins, an animated DreamWorks movie scheduled for release in 2018, which he is also directing.

Set in the Australian outback, Larrikins centres on an anxious little bilby called Perry and a kangaroo called Red.

“The kangaroo is hard-edged and unemotional, thinks everything is a bit of a joke, hates authority and all that good Aussie stuff – though it’s very important to me that the movie moves us beyond that,” says Minchin.

“Perry is an OCD, hyper-controlling, very fearful, very kind little dude compulsively stacking berries all the time. They go on this massive road journey together and Perry has to learn to be brave and Red has to learn to be more caring. It all sounds quite twee but it’s actually very funny. There are lots of laughs in it. The term Larrikin is used, but its definition is actually only obliquely discussed. We never clearly define it, that’s part of the charm of the word – it’s kind of ambiguous.”

“It’s an Australian story and I’m writing very much as an Australian writing about Australia,” adds Minchin.

As you’d expect, he will be making some political points along the way. There’s a song called Proper Aussie, for example. “It’s sung by Howard the crocodile, who is a bureaucratic bully in charge of a bit of river that our heroes have to cross. He sees his job as preventing ‘non-native species’ from spreading. It’s quite fun because we get to talk about fauna issues as well as xenophobia,” says Minchin.

On top of all his composing, Minchin has managed to find time to take to the stage himself in recent years. In 2012/13 he turned in a sensational performance as Judas in an arena production of Jesus Christ Superstar, which toured around the UK and Australia.

In 2013, he also co-starred with long-time mate Toby Schmitz in Tom Stoppard’s Rosencrantz and Guildenstern are Dead for Sydney Theatre Company. On screen, he has just been seen as the odious Smasher Sullivan in the ABC’s acclaimed mini-series The Secret River, based on Kate Grenville’s novel about the early days of Australian colonisation.

He’s keen to do some more acting. However, he’s unlikely to have time for much theatre in the immediate future, given the demands of Groundhog Day and Larrikins.

“I want to act more but I think it’s more likely to be a few eps on a TV series or a cameo role in a film,” he says. “I’m interested in film and TV now. It’s all weird and a slightly sitty-around industry but it’s great to be a part of something, to do these little scenes and then see it all put together.”

Then there are his solo shows. He had 10,000 people across two nights eating out of the palm of his hand when he performed at the Sydney Opera House in February but, again, it’s a challenge to find the time.

“I think I can do it all,” he says. “I just need to manage my time and not lose my mojo. Comedy is a game of fearlessness and you’ve got to do it lots to stay fearless. I kind of had a wobble last year when I first went back after two years of not doing a solo show. I found it hard. I’d forgotten that you can’t just wander up. You’ve got to get your chops back up. It’s not something that comes with no work, the fast lyrics and all that stuff. But it’s worked out all right.”

Minchin, his wife Sarah and their two young children Violet and Caspar now live in Los Angeles after a decade in London, where his fame had reached the point that he was recognised pretty much wherever he went.

“LA was a lot about the film (Larrikins) and a lot about knowing that I had to leave London one day because it was just getting harder and harder. And also about coming home (to Australia) eventually. So LA is meant to be a stepping stone,” he says.

It was while he was living in Coogee during the STC season of Rosencrantz and Guildenstern that he decided he wanted his kids to grow up in Australia.

“The Larrikins thing was initially a songwriting gig then they said, ‘would you like to direct it?’ So I said to Sarah, ‘maybe this is our window out.’ It was awful leaving London. It was really, really hard, for Sarah particularly, but LA is kind of fun. We’ve met some really great people. You can drive around in your car. It’s a bit more like living in Perth. (Our house) is not a big place but it’s got a comparatively big garden with a pool and our kids haven’t been sick since moving there.

“People in America don’t really know me apart from Californication (the US TV series in which he played a coked-up rock star) though I was stoked that Spielberg and those people know exactly who I am. That’s their job to know who everyone is, and I am directing a movie for Jeffrey Katzenberg.

“So I’ve been shocked to realise it’s a perfect balance. I don’t get recognised in the street but the people who matter are keeping an eye on me. I sit in my room all day with a piano and when the kids come home I’m there. That’s why we moved to LA. And we can go to the shops and no one cares.”