Moonage daydream: Duncan Jones (formerly Zowie Bowie) steps into the limelight with his directorial debut

Fate is a funny thing as Duncan Jones, David Bowie's son, is starting to discover. Jones has never had any desire to be in the spotlight. "I saw the drawbacks of fame as a kid," he says. "It wasn't for me." In fact, for most of his adult life, he has gone out of his way to avoid it. And yet the man once known as Zowie Bowie now finds himself exactly where he didn't want to be – the centre of media attention.

It started in January when the 37-year-old attended the Sundance Film festival for the premier of his directorial debut feature film Moon, an atmospheric sci-fi drama, which stars Sam Rockwell as a lonely astronaut mining helium-3 on the lunar surface (Kevin Spacey provides the voice of Gerty, the robot). The film sparked the all-important buzz at Sundance and was quickly snapped up by Sony Pictures Classics. Next week Moon will have its first UK outing when it screens at the 63rd Edinburgh Film Festival.

Hannah McGill, the festival's artistic director, describes it as "a hot ticket. There's already a colossal amount of internet buzz about it," she says. McGill acknowledges that while there is a certain amount of intrigue around Jones, "when you watch the film you're not sitting there thinking 'goodness this is an interesting film David Bowie's son's made', because it's good in its own right."

What it means is that Jones will find it increasingly difficult to remain anonymous for very much longer. "I don't think things will change that much," he says, nervously. "I mean, I can understand the interest. It was always going to happen with the first film. Hopefully, by the second or the third film, who my father is won't be a story anyone's interested in. They'll either like the films or they won't and if they don't like them I won't be making them any more," he laughs.

According to McGill, he needn't worry. "The film shows such a sure hand as a director because it's a complicated film and to have one actor and do so much in terms of atmosphere and setting on what is a small budget and to make it work shows a great deal of skill."

Based on an original idea of Jones's and scripted by Nathan Parker, the director is "incredibly relieved" that audiences so far like the film. "There was so much riding on it for all of us," he says. "You only get one shot to do a first feature. So the plan was to try and make something that stood out. And I'm a huge sci-fi fan. I'm a bit of a geek, actually," he grins. "So I always wanted my first film to be science fiction. And the idea of finding alternative energy sources I've always found fascinating, as far as trying to get ourselves off fossil fuel. Fusion power is something I've always been interested in. And airships I always thought were really cool."

It's hard not to like Jones. He's intelligent, with a quick, self-deprecating sense of humour. His down-to-earth manner belies his privileged background, which included growing up in New York, Australia, Switzerland and Japan. He might have inspired his father's hit song "Kooks", but Jones has perfected the art of blending in. Dressed in a pair of nondescript jeans, shirt and parka ("like the one Kurt Russell wore in The Thing"), you'd never guess he's the son of one of the most famous musicians of the 20th century. Which, of course, is just the way he likes it. "That's why Sundance was so terrifying," he laughs. "The attention was overwhelming. I lost five kilos in 10 days I was so stressed. [On top of that] one of my biggest concerns was whether or not sci-fi fans would like it," he says.

If that wasn't enough to contend with, his father decided to fly in "as a surprise" to attend his son's very first film premiere. "That was terrifying for all of us to be honest," he says. "But it was also absolutely lovely and he loved Moon. It was quite emotional for both of us because he's been waiting for me to get off my arse and do what it is that I'm going to do with my life. At the Q&A afterwards I thanked him and said that I really appreciated that he gave me the time to work out what I wanted to do, because it's taken me a while."

Not that Jones has been sitting around idly waiting for something to drop into his lap. "I've tried lots and lots of different things," he admits. There was a stint in the games industry, for example, and before that he was working on his PhD in philosophy at Vanderbilt University, in Nashville Tennessee. "I know, I know," he laughs, holding up his hands. "What are you going to do with that right? Well, I have no bloody clue. I'm a hopeless romantic and I followed my girlfriend at the time. She was at undergraduate university and she went off to do her PhD in psychology. I didn't know what to do with myself so I went off to do my philosophy degree. But obviously that didn't work out."

He also worked for a time at Jim Henson's Creature Shop. (Henson directed his father in Labyrinth). "It sounds really glamorous, but it wasn't, because the job I had was mixing latex," he says. "To be honest, for ages and ages I didn't know what I was going to do with myself. And I put a huge amount of pressure on myself. I went through that whole thing of reading everything like What Colour is your Parachute? and I did everything possible to work out how I fit in. It's been a long circuitous route to directing."

The funny thing is that, although Jones fell in love with film-making as a child, he didn't pursue it till much later. "Because it almost seemed too obvious that that was what I was going to do," he says. "When I was a kid, as a hobby Dad and I used to make films. I was six or seven and we used to do little one-stop animations with Smurfs and Star Wars figures. And I used to be on sets when I was growing up. But it was too in my face. So it seemed a good idea that I go off and discover what else there was to do. It never occurred to me that I would end up back in film."

Jones is extremely close to his father and proudly acknowledges that he has been a "major influence on me". But it was Tony Scott (Top Gun, Days of Thunder) who convinced him to go to film school. "At the end of university I had the opportunity to work on something my dad was doing with Tony Scott," says Jones, "the TV show for The Hunger."

"It was like an eight- or nine-day shoot and I was under Tony's wing for the entire time. It was fantastic because it was basically like a condensed film-school masterclass. I just followed him around. He was constantly talking to me and answering my questions. That's when I knew what I wanted to do. And Tony said: 'Look, if you really want to do this, go to film school – but the real film school is commercials. So go and do that for a few years.'"

Jones joined Beattie McGuinness Bungay, "about four years ago", as a "creative". In 2006 he made his directing debut with a racy little commercial for French Connection, which depicted two gorgeous women fighting and kissing. He was heralded as the new wunderkind of the advertising world. Jones had finally found his calling.

"I hope to juggle both films and commercials in the future," he says. "I like both, although I was so focused on Moon I didn't have the opportunity to enjoy the experience," he says. "It really was ambitious. The amount of effects we had for an indie film was insane. But I think we've done something impressive. Moon is a little British independent jewel. I'm proud of it."

He's also proud of the fact that he never once threw his father's name around to get to where he is today. He has achieved it on his own mettle. "Although it's taken me a lot longer," he acknowledges. "But I think I've waited the right amount of time to do what I'm doing," he says. "I think if you're young and you're being compared to a successful family member, it's really hard to maintain any kind of sense of self-worth and credibility."

Not that he wants to "talk about that today". It's all in the past. Jones now has credibility both as a commercials director and a film director. "I know everything could fall apart tomorrow," he says. "Moon isn't even out yet in the UK but I am excited to see what happens next." It was recently announced that Jones will be at the helm of submarine thriller Escape from the Deep, but that doesn't start filming until 2010. So the first cab off the rank will be another sci-fi flick called Mute, based on another one of his original ideas.

"I don't only want to do sci-fi, but it looks like the next one will be sci-fi," he admits. "But you know Ridley Scott got away with it. He did Alien and Blade Runner and then did other things."

'Moon' is due for released in the UK on 17 July. Edinburgh Film Festival runs from 17-28 June

Edinburgh film festival

Starting on Saturday and continuing throughout the Edinburgh Film Festival, up-and-coming director and screenwriter Leanne Welham, whose film "Transgress" is being shown in the UK Shorts 1 collection on 26 June will be blogging from the heart of the festival activities. To read all the industry gossip, go to independent.co.uk/edinburghblog