“The first cut he showed me, I puked,” says Mathangi “Maya” Arulpragasam, AKA MIA, “and then I was ill for like four or five days.” She was watching a rough cut of Matangi/Maya/MIA, a documentary about her made by friend Steve Loveridge. The film makes extensive use of MIA’s own home movies. “It was awful when I watched it, the shock of it was insane,” she continues. “The shots with my mum, and us in the bedroom. And there was much more footage of my brother, which was really tough during those times. It still makes me emotional to think about it … ” Her voice trails off. She wipes tears from her eyes: “Yeah, it was very emotional.”

We are in a hotel suite in London. Loveridge is sitting beside her. “Very emotional,” he agrees sympathetically. “Because Maya hadn’t watched the tapes back for years and years.”

“No. I had never watched them back,” MIA cuts in.

“So it was a long time before I showed Maya another cut.” Loveridge says. “I was like: ‘That didn’t go well.’” They both start laughing.

MIA and Loveridge have been friends since they were art students in London 20 years ago; two outsiders drawn together, albeit from very different backgrounds. MIA is famously the daughter of a Sri Lankan Tamil resistance leader, and emigrated to London when she was 10; Loveridge grew up in Surrey. “Whenever you went round Maya’s house in those years, there were always incredible amounts of drama happening,” says Loveridge. “So it wasn’t like she was like a normal teenager who’s just obsessed with themselves. Her brother was going to a young offenders’ institute and she wasn’t going to see him for two years, and then her dad came back after no one knew whether he was alive or dead for 10 years. No one had heard a peep out of him. So they’re big family events. For ages, Maya called my film Keeping Up With the Arulpragasams.”

When Loveridge screened the finished film at Sundance earlier this year, MIA didn’t puke, but nor was she unequivocally happy with the result. “He took all of my cool out,” she said at the time, bemoaning the lack of focus on her music. “It’s not the film I would have made.”

That’s the trouble with MIA: there is no single way to tell her story. She doesn’t fit the formats. On the one hand, hers is the story of a self-made artist whose abrasive, lo-fi rap tunes and neon guerrilla stylings encapsulated a global cultural moment, especially via her ubiquitous hit Paper Planes. Taking another angle, it’s the story of an immigrant teen dealing with the drama of her fragmented family and learning to survive in xenophobic 80s Britain. There is also the activist MIA, who uses her position as the world’s most famous Sri Lankan to highlight the ongoing turmoil back home, and the plight of refugees and immigrants worldwide. Yet none of these angles quite captures the brash, fearless, defiant personality who has routinely energised and scandalised pop culture: performing at the Grammys with Jay-Z and Kanye West, heavily pregnant, in a see-through dress; being vilified for a video showing ginger-haired children getting shot in the head; upstaging Madonna by raising her middle finger at their 2012 Super Bowl half-time show (in the film, we see her getting told off backstage, then running away like a naughty schoolgirl).

Faced with all this, the challenge is to either make sense of MIA or simply decide that she doesn’t make sense. Many have settled for the latter, but that was never an option for Loveridge. As its three-part title suggests, rather than picking one strand, Matangi/Maya/MIA tells fragments of the whole story. The aim was not to explain MIA’s life but to provide context: “When you see it joined up into a narrative, it has different meaning. It’s suddenly understandable in different ways,” says the director.

Putting the film together took Loveridge nearly 10 years, including several false starts and a few crises of his own. MIA’s US record label (Interscope) and management (Roc Nation) were initially supportive of the project, he explains. “Interscope lined me up with loads of celebrities and channelled it into being a run-of-the-mill Behind the Music-style film,” says Loveridge. He conducted “hours and hours” of interviews with the likes of Kanye West, Spike Jonze, Danny Boyle, Romain Gavras, producer and ex-boyfriend Diplo, and Interscope boss Jimmy Iovine. But by 2013, frustrated by the lack of progress or funds, Loveridge had had enough. “I really couldn’t give a flying fuck,” he posted on his Tumblr. “Count me out. Would rather die than work on this.”

However, after a few personnel changes (MIA seems to go through managers like Spinal Tap went through drummers), Loveridge started afresh, ditching the celebrities and drawing instead on the extensive archive footage MIA had handed over to him. There was more than 700 hours of it, including those domestic scenes, suggesting that MIA had started work on her own bio-doc before her career had even begun. That wasn’t the case, although when Loveridge and MIA first met, she was as much a film-maker as he was. They were both on the film and video course at London’s Central St Martins college. “Jarvis Cocker and Pulp went to St Martins to do that film course before us, so that was the only saving grace,” says MIA.

This was the pre-digital era, when students learned on 16mm cameras and edited by hand. The college had one newfangled digital camera, MIA explains. “You had to sign and wait for a year to get it for 10 days. So when I got access to that camera, which was massive, I just filmed everything, cos you just never knew when you were going to get it again. I never thought that my family stuff was the thing; it was on the back end of tapes I’d shot where I was trying to make art films.

“I reckon about 70% of that film is shot by me, don’t you think?” says MIA to Loveridge. “Maybe about 10% shot by you. No, not even 10.”

“Yeah,” protests Loveridge. “Because some of that really early stuff is shot by me and you don’t even realise.”

MIA: “Which bit?”

Loveridge: “Bits of you putting your jacket on in your house, in 1997.”

MIA: “That is not shot by you!”

Loveridge: “It is shot by me. How are you shooting yourself putting a jacket on?”

MIA: “Because … ”

Loveridge: “You never had a tripod. You were too poor.”

MIA: “Yeah, but I had a shelf.”

There was other footage as well as the Keeping Up With the Arulpragasams material: MIA hanging out – and arguing – with her friend Justine Frischmann of Elastica, who became her entry point into music (MIA shot a video and designed artwork for them); and singing a demo version of Paper Planes with Diplo in her bedroom. There was also footage of MIA’s trip to Sri Lanka, post-college, in 2001. She got a small amount of funding from a TV company to make a documentary about her cousin, who was genuinely missing in action. It was only on arriving in Sri Lanka that she discovered that filming and conducting interviews could get her arrested. So she filmed her family instead. “I really wasn’t prepared in a professional kind of way,” she laughs. That much is confirmed by a clip of MIA setting off from London and forgetting to take one of her cameras, which is still filming her.

At this point, MIA pivots to the serious abuses still going on in Sri Lanka nine years after the civil war officially ended: the 100,000 missing persons still unaccounted for; the mothers still lobbying the government for answers; the irony of her US and UK taxes supporting foreign policies that she opposes. She talks about US influence, Facebook’s connections to Sri Lankan politics, Cambridge Analytica, Wikileaks, Edward Snowden and her former friend Julian Assange (“He has sacrificed so much for belief in truth”).

There is rarely space to accommodate her as both a pop-culture figure and a political activist, yet it is MIA’s mission to combine the two. I turn the question to the director: was there a reason not to focus more on global politics in the film?

“Good question,” says MIA triumphantly, turning to Loveridge to await his response.

“It’s a very complicated story to tell,” says Loveridge, “because the things that Maya is saying need backing up, to not leave her vulnerable to being accused of being paranoid or a conspiracy theorist. And it started to become a completely different film where I’m investigating the Sri Lankan government’s collusion with major social media outlets and 45 minutes ago we were dealing with Justine Frischmann and Elastica.”

Perhaps MIA needs to make her own film. She is taking steps in that direction, having directed her recent music videos herself, such as the epic, migrant-themed Borders, filmed in south India.

“Yeah, I definitely want to try to make a film,” she says. “I keep writing and then stopping cos I get taken into supporting Steve’s film.”

“I just had to rip her away from the typewriter,” says Loveridge sarcastically. “Maya is really into epic sagas. When she reads me her films I’m like: ‘That’s going to cost a fortune.’

There is still time. Most musicians get a doc when their lives or careers are over, but MIA is still only 43. She certainly sounds keener on making films than making new records: “I think I’ll always make music, with people I like making music with, but I can’t do it the way that it demands a female to do it right now. I can’t be bothered to get lip injections and a fake butt and a pair of fake tits.”

“But musicals … ” Loveridge suggests.

She looks at him quizzically.

Loveridge: “ … I think are in a right slump, and I think that would be amazing. We did this art biennale in Kochi in south India, and Maya was invited to exhibit as a visual artist but also perform there, and it was the first time I’d ever seen you work with Tamil drumming and it was so incredible. That I’d just love to see.”

MIA: “As a musical?”

Loveridge: “Yeah. I just think that would be the most incredible thing ever.”

MIA: “Wow. No, I’m writing, like, a Chinese epic.”

Matangi/Maya/MIA is in UK cinemas from Friday 21 September