In a fifth-floor flat of a tower block near Père Lachaise cemetery in Paris, 50-year-old Ibrahim Ag Alhabib, the co-founder of the brilliant African “desert blues” band Tinariwen, is talking about the first time he heard music. Well, he’s telling a friend, who’s translating from Ibrahim’s Tamashek language into French. Then the friend tells Ibrahim’s Bristol-based manager, Andy Morgan, who translates from French into English. As the three men speak, the smell of sweet tea drifts through the spartan apartment (Ibrahim appears to be sleeping on the floor). He is in Paris for a couple of European interviews, before appearing at Glastonbury this weekend, staying in this flat that belongs to a friend. He lives a world away, in the desert in Mali, so the tea is a nice reminder of home.

“I picked up on music very, very young,” says this leader of a band beloved of, among many others, Robert Plant and Chris Martin. “When I was 4 or 5 I saw this film at a bush cinema — people would arrive in a desert village with a projector. It was a cowboy film, and in it was someone playing country and western music on a guitar. I had a flash. I built myself a guitar from a jerrycan and a stick.”

This was 1963, around the time that Ibrahim’s village in the remote northern desert was raided by the army. Ibrahim’s people, the nomadic Tuareg, were resisting the postcolonial African elite who were running Mali from the distant capital of Bamako. The soldiers arrested Ibrahim’s father, accused him of aiding the rebels and killed him. Then they slaughtered the family’s camels, cattle and goats. Ibrahim, his mother and siblings, like many Tuareg, fled to Algeria.

In exile in Algeria and later Libya, Ibrahim became aware of the power of music. “I realised you could say something with words, you could really transmit some thought to the people around you. The first song I wrote was called Imidiwan — which means ‘friends’, ‘companions’. The message was: ‘Listen to what I’m saying. We’re all the same, we’re all in exile, we’ve left our country behind, but that’s where we belong.’ From the first song I wrote it was a way of talking to my community.”

Four decades later, Imidiwan is also the name of Tinariwen’s intoxicating fourth album. It’s a swirl of traditional North African music, blues and funk, underpinned by Ibrahim’s dextrous guitar playing. The vocals are an entrancing mix of female and male harmonies, sung in Tamashek. But wherever they travelled with their breakthrough albums, Amassakoul (The Traveller, 2004) and Aman Iman (Water is Life, 2007), Ibrahim was told repeatedly by people: “Your music speaks to me.”

He thinks the connection with Western music and tastes “is something to do with the emotion of the music, the solitude of the blues. We have a word, assif, which means the same as the blues — it’s pain, spiritual pain, longing, loss. So maybe it’s bound to sound the same.”

“We love Tinariwen,” Martin had told me as he showed me round Coldplay’s North London studio — and, sure enough, there was a picture of the African band in prime position on the wall-mounted mood board for Viva la Vida. “Tinariwen are fantastic,” Plant enthused last year when I interviewed him in Nashville. He raved about appearing at the Festival in the Desert, at which he shared a bill with Ibrahim and his ever-evolving band of musicians (there are eight who tour regularly, more who stay in Mali). This was “world music” in a proper sense, he said, rather than a marketing one. “If you get the DVD of it, it’s mind-altering,” Plant added. “Most [of the artists] were from North Africa, but there were a couple from France, and there was a Lakota Sioux speed-metal group from Arizona. And they really hooked up with the Tuareg guys. They’d both been shafted by imperialistic powers, French or these white Americans. Even some of their symbology, the Tuareg culture and history, was similar to that of the Lakota.”

Ibrahim and some of his friends in the band were soldiers for six months in 1990, members of a Tuareg rebel movement, after a brief stint in a desert army assembled by Colonel Muammar Gaddafi, the Libyan leader. He has spent some time in prison (and has the DIY tattoos to prove it). But since some members of Tinariwen (their name means the Desert Boys) first performed in Europe in 1999, he has fought for freedom in his songs. Imidiwan, which the band recorded in a portable studio in Ibrahim’s village of Tessalit, opens with a song whose title translates as My Friends from all Over Africa. “It’s a wake-up call” to the diaspora, he says. He’ll be playing it at Glastonbury.

It’s the band’s second appearance at the festival — their first was during one of the legendary muddy years. What did this desert nomad make of that? Ibrahim smiles at the mention of the word “Glastonbury” and lights up a second Dunhill. “I did make the link with the rainy season. When we were young we’d go down to the river, which suddenly became this torrent when the rains come. We’d have parties, sing songs, make fires, have little tents. And when I went to Glastonbury it was like that times a million.”

He won’t mind if it’s wet this weekend. “I like the rain,” Ibrahim smiles. “Rain is a beautiful thing in the desert. If there’s no rain it’s really serious.”

Tinariwen play the Pyramid stage at Glastonbury tomorrow. They release their album Imidiwan: Companions on Monday

Explore Music

• CD Reviews

• Live Reviews

• Classical

Editor's choice

• The 100 Best Films of the Decade
• 70 facts you didn't know about Marvel
• The 50 Biggest Movies Of 2010