Turner Prize nominee Marvin Gaye Chetwynd has serious fun with art

I'm here because she is – London became too expensive with a child so she headed to Glasgow after being told it was a terrific place to live and work – and because audiences in her adoptive homeland are soon to be given a flavour of her very particular talents courtesy of The King Must Die.

A newly commissioned work, it forms the centrepiece of the Edinburgh Art Festival and takes place in the old Royal High School, the building once described as "a nationalist shibboleth" when it was earmarked for the site of a putative Scottish Parliament. As she unfurls a plan of the place, my eyes make an associative leap to the blue and white Yes poster sitting on the mantlepiece. No prizes for guessing which way she voted, then. "I'm a risk-taker," she grins when I ask.

The King Must Die is based on Mary Renault's 1958 historical novel about the early life and adventures of Theseus. As well as being an installation, the exhibition features a daily performance by a cast of 10 and in its staging dips into the oeuvre of influential Czech artist and set designer Josef Svoboda. To that end, Chetwynd's studio next door is currently crammed with papier mache palm fronds and what looks like a giant cardboard turtle.

The third element to the piece, of course, is Chetwynd herself, and an artistic imagination which for some years now has seen her stage carnivalesque live performances using home-made props, sets and costumes. She gives these shows titles like Help! I'm Trapped In A Muzuzah Factory and they're tied together with references drawn from every corner of the cultural galaxy. Yes, even Star Wars: her 2003 work An Evening With Jabba The Hutt featured a papier mache replica of the corpulent alien gangster surrounded by bikini-clad women.

She got her Turner nomination for Odd Man Out, an exhibition at London gallery Sadie Coles HQ which was essentially a five-hour performance on the theme of democracy. It also featured puppets of Jesus and Barabbas and drew on elements from The Grass Is Singing, Doris Lessing's acclaimed 1950 novel about racial tension in Southern Rhodesia.

If any of this makes you want to laugh, that's fine up to a point: fun is the name of the game as far as Chetwynd is concerned. Fun is how you sneak in the big ideas. One of her most recent commissions, for example, was to design a soft-play area for a leisure centre in Barking, a task she threw herself into with her customary gusto. So now, as Barking mums and dads sip coffee and scoff tray-bakes, their offspring swing around a monochrome play area decked out in designs suggested by the Dagenham Idol, a 4000-year-old Bronze Age fertility symbol.

The King Is Dead is no less serious or playful. It's a humourous meditation on ritual and the power of collective emotion, as well as a celebration of ambience. To that end Chetwynd wants to light her foliage in such a way that the leaves throw great shadows across the space. "A sort of Magic Flute-style operatic setting," is how she describes it. "The leaves are great when you shine light through them because the shadows are really sharp and illusory. So however bad my papier mache is, when the light is set the effect is really quite glamorous and sumptuous and gorgeous."

Her collaborator is a lighting designer she met by chance at a gallery opening. Her "cast" are mums from Dragan's playgroup, some fellow artists and other "random" friends she has made since moving to Glasgow two years ago. I have to ask, then: do you just go around collecting people?

She laughs. "I'm quite direct and I think that's all it takes, to be honest with you. I've got very quick wiring. I don't hesitate. I think if you hesitate and then you become anxious that you might be being tactless or rude or something, then things won't happen. I really don't hesitate with anyone – oddly it seems to fit with living in Glasgow. A lot of other people here are the same. Even on the bus. They've got the same thing, the same wiring."

She returns to the subject a few minutes later, as if she has been chewing on it while the conversation has been elsewhere.

"You say it's collecting people. I don't know if it's that or seducing them or winning their trust. But however it works, they're willing to play with me and come and have fun in Edinburgh."

There's that word again: fun. It's a good word to describe her, too. Others would be engaging, thoughtful, clever, unconventional and pleasingly Bohemian.

Those last two qualities certainly sum up her childhood. Her father, Rupert Chetwynd, had been a Lieutenant in the Grenadier Guards and is related to nobility. You can look him up in Burke's Peerage. Her mother, Rupert's second wife, is Luciana Arrighi, daughter of Count Ernesto Arrighi, an Italian diplomat who had served under Mussolini. She's a set designer of some renown who started out working with Ken Russell and John Schlesinger in the 1960s and later worked with Ang Lee, Norman Jewison and Stephen Poliakoff. She won an Oscar in 1992 for her work on the Merchant Ivory epic Howards End and a Bafta for HBO drama The Gathering Storm.

As kids, Chetwynd and her elder brother were shunted from country to country and film set to film set, sometimes attending school and sometimes not. I ask her if it's true she couldn't read until she was 10. It is. Her dyslexia didn't help but that's not the full story.

"I can't really explain it," she says. "And now I'm a parent myself I can't really understand what they were doing, unless it was an experiment. But we travelled a lot because of my mum's work and my dad's, so there was endless uprooting from schools. But loads of time we just didn't go to school. We'd play on a beach or in our camper van."

She describes her parents as "extreme meritocrats" who "earnestly wanted their children to be interesting people" and took a dim view of mediocrity. "If someone's not intelligent, they literally would not mind it if they were killed," she says.

To that end, she and her brother would be given endless challenges such as swimming in rivers full of snakes. In one sense it backfired. "My politics are almost the opposite," she says. "I'm extremely compassionate and sentimental." In another it didn't. "They wanted us to be brave people so now, ironically, I'm also stuck in something I can't get out of because of the way I've been brought up. I am really brave. I am ridiculously fun and experimental." Mind you, she adds, "I don't want to do that to my son."

That camper van also doubled as her home for a time but when Chetwynd was nine the peripatetic childhood came to an end and the family wound up in London. Aged 11, she was sent to Bedales, a public school in Hampshire where near-contemporaries included Lily Allan, Sophie Dahl and Kirsty Allsop. Aged 13, she was "asked to leave". "I had a lot of fun," she says. "That was the problem."

She ended up at a Catholic girl's school and then a sixth form college. From there she won a place to study social anthropology at University College London. She followed that with a second degree at the Slade School of Art, and an MA in painting at the Royal College of Art, graduating in 2004. By then, she was already gathering a cult following for her underground "happenings" and gallery-based shows.

Another attention-grabbing hallmark of Chetwynd's art is that many of her performances and films feature nudity, often hers. When she was nominated for the Turner Prize, The Daily Mail delighted in the fact that the "wacky" artist was currently living in "a nudist colony next to a cemetery". It's all true.

"I love the idea of nudity," she says. "I'm so not body shy." In part it's another way to scratch at prudery and taboo, but there is a philosophical underpinning to it. She tells me about her admiration for the Adamites, an early Christian sect best described as anarcho-nudists who sought to return to a prelapsarian state and were later deemed heretical by the Catholic church.

"That's where I'm coming from. I'd like to make a decision to say that you can ignore the Fall of Man and all of the problems of being human and go back to a state of innocence. And the nudity comes with that. It's super-naive and pathetic, but I genuinely have that desire."

Finally, then, to the elephant in the room: her name. Spartacus was part joke and part game, she says, a response to claims she was a faddish artist who would rise fast and crash just as quickly. It was a kind of "incantation" or "spell", she says, a way of making herself a "shield" by using the hardest name she could think of – Spartacus: gladiator, rebel, hero. "I feel like I was naive about how irritating it would be for people," she admits. "They thought I was making them enter into some sort of performance by making them call me Spartacus. I'd never thought about that."

The second (and, she insists, final) name change was prompted by motherhood. "I realised the personal life, the family life is so key that I've really got to protect it," she says. In this, the story of Marvin Gaye – shot dead by his father – was powerfully instructive. So she took his name as a talisman. "It makes me keep the most valid thing focussed, so it's like a private message for me. The name must remind me not to be corrupted or run away with my work and to remember to prioritise my family and not f*** them up."

Kind of a knot in your mental handkerchief?

"Exactly," she beams.

And, after all, what other kind of handkerchief would do for a naked artist having fun in the Garden?

The King Must Die is at the Old Royal High School, Regent Road, Edinburgh, July 30-August 30, 10am-6pm (performance times vary) as part of the Edinburgh Art Festival, www.edinburghartfestival.com