We all love our mobile phones, and the smarter they get, the more we want them. There is, though, a dark side to this affair. In the Democratic Republic of Congo, our demand for phones has been helping to finance a civil war which has killed more than 5m people. There is, according to the title of Danish director Frank Poulsen's eye-opening documentary, blood in the mobile. Minerals from mines under the control of warring factions have been making their way into our mobiles for years. The UN raised the issue a decade ago. But even though it involves more of us than, say, blood diamonds, how many of us know about it?

"I knew there was a war in Congo, but I didn't know it had anything to do with my phone," says Poulsen. "I think we often forget, or maybe don't know, how closely connected we are. Things that go on in Africa seem to be very far away and have very little to do with us, but it has a lot to do with us. My mission, as a film-maker, is to make these connections."

Poulsen arranged a research trip to Congo and successfully secured entry to the Bisie mine, located deep in the jungles of Walikale, where thousands of people, many of them children, were living and working in hellish conditions. "I have never seen anything like this," says Poulsen. "This was really terrible." Guards on a makeshift gate levied "taxes" on people going in and coming out. "And that's how simple it is," he says. "These armed groups are really stealing money from the poorest and most miserable people in the world."

Inside the gate, conditions are "medieval". "There's no clean water anywhere. There's thousands of people, and you think: 'How do they survive here? How can they do this? How is it possible?'" Children as young as 12 work as deep as 100 metres below ground, and Poulsen tried seeing for himself what conditions were like inside the mine, but he didn't get far. "I was simply too big and I had a camera that made it hard for me to get an everyday life atmosphere. People would just sit and look at me."

The second – and final – time he visited Bisie, he gave a small camera to a young boy. The haunting images he captured, of men and children chiselling at rocks, grimly hark back to an age that seemed long gone, when Leopold II of Belgium ran the Congo as a private slave colony.

In an attempt to connect the dots between the mine and the phone industry, Poulson approached Nokia – as well-known advocates of corporate social responsibility, he thought they would be keen to show him what they were doing to improve the situation. They told him by email that they didn't have the "resources" to help him. He says he rang them once a week for almost a year, trying to arrange an interview with someone in power, but found himself fobbed off at every turn. When he did eventually get access, it was to mid-level people whose apparently sincere desire to do the right thing was not matched by their ability to make actual changes.

"Nokia had the chance of being the hero of this film, if they had opened up to me. It is a mystery why they didn't. But it also shows why this issue isn't being solved: people are turning a blind eye."

Blood in the Mobile arrives in the UK at a time when recent legislation passed by Congress in the US requiring more transparency in the extractive industry seems to already be making an impact in Africa, even before its implementation. Similar legislation is now being sought at an EU level. "We can't leave it up to the companies themselves to solve," says Poulsen, "because they have had a fair chance at it."

The casualties of war in the DR Congo have been, he says, like a "Haiti earthquake every third month for the last 15 years. This is an extraordinary problem, a catastrophe that we have to address right now. There are too many people dying."

• Blood in the Mobile is released on 21 October