Australian composer and comedian Tim Minchin, 42, was born in Northampton but raised in his parents’ native Perth. After an award-winning comedy career, he wrote the music and lyrics for the Royal Shakespeare Company’s global hit musical Matilda, followed by the stage musical adaptation of Groundhog Day. He lives in Los Angeles with his wife, Sarah, a social worker, and their two children.

Tell us about your new children’s book, When I Grow Up, which is based on the lyrics of the song from Matilda.
It’s awesome – I didn’t even have to do anything [laughs]. That’s the incredible thing about Matilda, it keeps manifesting itself in different ways. It’s profoundly gratifying to have something else beautiful put into the world that was sparked by something you wrote eight years ago.

Did you test the book on your own children?
I’ve shown them it, but my kids are pretty unimpressed by me. They’ve never seen me do comedy or a concert. All they know is that I do “quiet work” or “loud work”. Quiet work is writing, loud work is performing. They’ll ask: “Are you going out, Dad?” and I say: “Yeah, I’ve got loud work tonight.”

Do your kids know you’re famous?
Not really. The horrible F-word doesn’t get used in our house. If someone recognises me and the kids ask why, I just say they know my work. One of the reasons we moved to LA four years ago to make an animated film [musical comedy Larrikins, which was recently cancelled by DreamWorks after Minchin worked on it for several years] was to arrest any chance of me becoming too well-known. And that really fucking worked. It worked too well. I screwed my own career. I sometimes think: “What have I done? I’d just done an orchestral tour and could’ve spent the last four years being a rock star rather than talking to studio execs.”

I’m guessing your Hollywood experience hasn’t been good?
You could say that. I’m slowly recovering from the slings and arrows of outrageous Americans. The film getting shut down was awful. It really knocked me sideways. I’m grieving the loss of time and art. Don’t worry, though – I know I’m banging on, sounding bitter and spoiled, when I’m actually the most privileged person in the world.

So you’re swapping America for Australia?
Yes, we’re moving to Sydney at Christmas. It was always the plan to go home for when my daughter starts high school.

You played some live gigs in London this week. Do you miss it here?
Very much. London’s my favourite place. I lived in Crouch End for years and come back as much as I possibly can. I miss touring, too. The plan for next year is to get back into it and create a new live show. I’m interested in how the world’s changed since I last properly did comedy in 2010.

What’s been your view of that from over in LA?
Pretty bleak. It feels a bit post-jokes. Maybe “Post-Jokes Jokes” should be the name of my next live show. In this post-factual era, the horse called “evidence” seems to have bolted. That horse is in the knacker’s yard. California is obviously a liberal heartland but I really have a problem with this country. They call it populism, but it’s just nationalism. In a global world, nationalism is a fantasy and it’s poison. It used to be appropriate but it’s not any more and we haven’t learned that lesson yet. Trump is a nationalist. Brexit wouldn’t have got across the line without nationalistic philosophies. Even Australia’s stubbornness about gay marriage, which is as upsetting as everything else at the moment, is a sort of nationalism.

You recently posted a song on social media titled I Still Call Australia Homophobic. How would you feel going to live there if the law doesn’t change?
I have to believe it will get passed, but the plebiscite has already done its damage. The stupid fucking postal survey [to gauge public opinion] is just the prime minister trying to placate these idiots who are on his back, but it’s indistinguishable from deliberately trying to hurt the LGBT population. Families with same-sex parents have spent six months with this bigoted shit coming through their letterbox. The whole disgusting circus makes me want to scream. Whichever way the vote goes, these people have revealed themselves. I don’t think they’re evil, it just means we’ve got a long way to go.

Is there still a film version of Matilda in the pipeline?
Yeah, but it’s a pretty thin pipe, so we’ll be squeezing our way through it for a long time.

Bertie Carvel, who played Miss Trunchbull in Matilda on stage, is currently causing a stir in BBC drama Doctor Foster…
Bertie’s an incredible actor. He can go from evil headmistress to sexy bastard. Now he’s Rupert Murdoch in Ink. He’s a rare creature who takes his parts very seriously and makes careful decisions about what he’ll do next. It takes strength to run your career like that.

Your Groundhog Day musical just closed on Broadway. Is it heading back to the West End?
It’s my favourite thing I’ve ever been involved in. I’m very proud of it. Hopefully it’ll be back there soon and we can’t wait. It went down well in New York – critically acclaimed, nominated for seven Tonys, ran for six months on Broadway – but it’s a tough town at the moment. There’s a post-Hamilton bottleneck so it’s a slaughterhouse of competition, like the Red Wedding from Game of Thrones.

Aren’t you also about to join Robin Hood’s Merry Men?
I’m playing Friar Tuck in a crazy big Robin Hood reboot that comes out next autumn with Jamie Foxx and Taron Egerton. That’s going to change my life again. Or maybe it’ll sink without trace (laughs).

What else are you up to at the moment?
Loads of bitty things. You “take meetings” in LA and I’ve been taking meetings about acting gigs. I wanted to stay behind the camera for ages but now I’m considering some sort of comedy vehicle. I’m writing a new, non-comedy album. I’m about to shoot a still-embargoed TV show in the UK, which I can’t tell you about or I’d have to kill you. There’s some films I’m writing songs for. So I’ve got my fingers in more pies than a Bake Off contestant. I’ve always been like that. One of the great heartbreaks of the last few years is that I let myself get sucked into this massive project. All my eggs were in one basket, whereas my favourite thing about my career is its variety.

I saw you described recently as “the world’s favourite ginger”. Are you?
Trouble is, I’m not a real ginger. I’m just a ginger-bearded, pale-skinned, strawberry blond. I have a ginger vibe about me but can’t put myself in the Damian Lewis/Ed Sheeran/Rupert Grint league. I’d feel fraudulent. I don’t reckon I’m in the top 20, if for no other reason than a basic lack of red pigment.

• When I Grow Up by Tim Minchin, illustrated by Steve Antony, is published by Scholastic (£12.99). To order a copy for £11.04 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99