Stereolab aren’t on the same page about why they’re touring again after a nine-year hiatus. “We’ve got seven albums coming back out...” says Tim Gane. “For the money,” Lætitia Sadier says simultaneously. They are the core duo of one of the best bands of the turn of the century: blending lounge-pop, punk, tropicalía and political poetry, they stuck out like a sore thumb during the Britpop era.

As Gane says, most of their albums are being reissued. But the pair were in a relationship for 16 years, separating in 2004; they weathered the sudden death of their bandmate Mary Hansen, and years of touring that Sadier describes as “crushing and exhausting”. So perhaps her deadpan cynicism has a grain of truth.

As they embrace in a south London pub, Gane and Sadier’s affection is stiff and polite. They met in Paris in 1988, when Sadier went to see Gane’s band McCarthy. “What I found attractive was the lyrical content, which was heavily political and super twisted,” she says. “I saw what the power of music was, through lyrics, to change the world.” France was “disappointing. British rock music is much more interesting, much richer, and closer to your reality: the pub, with a venue, and you do a ‘gig’. It’s a three letter word. In France, you do a ‘concert’ – you’re on a pedestal.”

Gane was frustrated with not having more creative control, and began Stereolab with Sadier after she saved up to move to London. “Tim said: why did you save up all that money? We can sign on. I went to the dole office and was like, really? Unheard of!” Gane says the dole “maintained 90% of bands. I’ve never had a job, never done a job interview in my life.” The pair started writing songs instead, their favourites from nearly 20 years picked out here.

An early publicity shot, from 1991. Photograph: Photoshot/Getty Images

John Cage Bubblegum (1993)

The title sums up the band’s MO: avant garde pop. “We were trying to make what I called juxtaposition: a montage, or collage, to see how one thing influenced another,” says Gane, who wrote all the music. Sadier agrees. “We were quite informed by Dada. They were about putting one thing against another and seeing what happens, and maybe you find a deeper truth in that collision.”

Thanks in part to a broken Farfisa organ that would only let them play two-note chords, the juxtaposition was of minimalist synth drones, motorik drums and guitars, and mellifluous vocal melodies from Sadier. “In this instance the lyrics were more poetic than political, it’s just about a beautiful and sad landscape,” she says. “But [1994 single] Ping Pong is very overtly political – about the economical cycles of capitalism inevitably leading to war. People thought: great pop song! And then heard the lyric and felt really slapped around the head. I think that’s kind of cool.”

Jenny Ondioline (1993)

The band gained traction as outliers between Madchester, techno, shoegaze and the beginnings of Britpop. “The shoegazers were what Margaret Thatcher produced: really shy, non-expressive, dull, lots of pedals, no energy,” Sadier says. “For us it was a very derogatory term.” Although Gane thinks he might have inadvertently invented it, playing with the band Moose. “I got in the tour van without putting my shoes on – I just had these fluffy grandma slippers. I had to play a gig in Glasgow, and spent the whole time looking at my slippers thinking: these are ridiculous. Then there was a review that mentioned ‘shoegaze’.”

In contrast to that genre’s non-committal haze, the 18-minute Jenny Ondioline was their ultimate use of the steady, expansive motorik rhythm pioneered by 70s German band Neu!. “Motorik was the total inverse of technique,” Gane says. “You don’t have to be a good drummer – you just don’t change. But for good or bad I’m very attracted to melody, even in the most avant garde machine noise.”

Its lyrics are an inspirational screed on never giving up in the face of fascism. Sadier had grown up as Jean Marie Le Pen’s far-right Front National gained traction in France, and prime minister Jacques Chirac privatised the French banking system, aided by Francois Mitterrand as president. “No true honourable socialist would privatise money, but he did. He knew he would get shit for that.” The song’s message still resonates for her. “We’re being crushed into ways of thinking and doing. And social media can really participate in that.”

L’Enfer Des Formes (1994)

This song is from the album Mars Audiac Quintet, which stepped the band’s popularity up a notch – they toured the US with the all-star Lollapalooza travelling festival. “That was a good experience,” Gane says brightly. “Got to see Beastie Boys every night.” He grimaces. “And the Smashing Pumpkins.” L’Enfer des Formes is described as “the Ramones song – that kind of slamming pop. There was this craziness, in getting lost and dizzy, and building up bits of intensity. And people really liked that, these things whipping around you fast.”

Sadier’s lyrics, in French, are about political apathy. “Walking away from our responsibilities, and I’m the worst one,” she says. “We’re governed by a system that had its time, it worked for a while, but now it’s not working for the majority of people on this planet. And we know this, but how do you unlock this thing in humans as a community? It’s this massive interrogation for me.”

Metronomic Underground (1996)

Gane hit a wall: the endless road suggested by motorik had finally run out. “It was a difficult time. There was bad feeling, a lot of relentless touring.” Sessions for the album Emperor Tomato Ketchup started badly. “It was bass and saxophone and drums playing nearly the same riff for eight minutes. The engineer was like: you’re going to sell three copies.” A breakthrough came when he remixed 60s psych band the Godz, and started looping one section of it: his whole songwriting approach suddenly changed, and the album Emperor Tomato Ketchup was built up not from driving riffs but interlocking looped patterns. The result is some of their funkiest, prettiest music. “It was like you’d come from a cave, or across a mountain, and there was another totally different landscape,” he says. “Like on the original Star Trek where every day you could look forward to going to a new star system.”

Sadier, meanwhile, had been reading the oracular Chinese text I Ching, which had helped her decide to move to London. “I asked the book: should I be doing this? And it was like: it’s going to be great! But it doesn’t always tell you that. It can tell you scary things. It’s a harsh book – it’s not about flattering who you are or making you feel good.” The lyrics to Ketchup’s opening song, Metronomic Underground, are appropriately meditative, and ponder the infinite. “The purer the connection you have to the universe, the more things are going to flow in your life,” she says. “And of course, the struggle is that there’s a system out there that doesn’t want you to connect to the universe or the forces of nature, because if you do so you’re empowered and you’re going to buy less shit.”

Simple Headphone Mind (1997)

Gane collaborated on this proggy epic with one of his “childhood heroes”, avant gardist Nurse With Wound. “Weird child!” Sadier laughs. Gane says this period of the band was “where everything you try kind of works. There’s no bad door – whatever one you go through, it’s another kind of greatness. It was a very ‘up’ period for me.”

Stereolab on Later … With Jools Holland in 1996. Photograph: Andre Csillag/Rex Features

The Flower Called Nowhere (1997)

This fertile period led into Dots and Loops, their most commercially successful album. I tell them that Pharrell once named The Flower Called Nowhere as his favourite song to have sex to. “To have his willy sucked to, actually,” Sadier corrects me. “So honoured!”

It’s one of Gane’s favourites, but he feels the album, their first made with computers, is “a bit too sophisticated. It gave it a bit much of a laid-back, ersatz feel. The computer has ruined rock music in a way, because it makes it too polite. It’s very hard to disagree with, and you have to. Sometimes you listen to records done in the 60s and they sound totally wild, going out of time, and when you lose that, you’re losing a bit of what makes something exciting. I find rock music now particularly boring. Hip-hop and electronic music have dealt with this problem [of computers] very, very well – rock music hasn’t.”

The Free Design (1999)

In Stereolab, Gane writes the music and Sadier the lyrics. “That was the contract that I did not know I was signing with Tim: that he would control the music absolutely and entirely,” she says. “There were other things in Stereolab that were frustrating me, too. It was always too layered – I would hear the songs on a four-track demo, and their power and their essence, and I felt: this is beautiful. There was a way of working that was very industrial, and mass produced, that was really driving me crazy. And we weren’t laughing that much.” So she formed her own side project, Monade. “It was quite healing to be in a band: ah, you can be in a band and have a lot of fun! And be really friendly and love each other! Not that we didn’t love each other in Stereolab, I think we did very much. But it was not really expressed somehow – people were grumpy.”

Gane bristles at the accusation of control freakery. “It’s not about control. It’s just very difficult for me to be involved in just one part of the music – that was what I had in my previous band and what was so frustrating to me. I can’t separate things.” They pressed on, making Cobra and Phases Group Play Voltage in the Milky Night, “the weirdest album” according to Gane. The Free Design is tropical Brazilian pop with Sadier pondering: “What crushes our desire not to be trapped?”

‘Like a sister’ … Mary Hansen at the window. Photograph: Brooke Williams

Baby Lulu (2001)

Tragedy struck in 2002, when the group’s second vocalist Mary was killed in a cycling accident. “She was a great spirit in the band,” Gane says. Sadier adds: “She was like a sister. I still feel like she’s with us – her spirit is very alive.”

“We just had to make a decision whether we wanted to carry on making music,” Gane continues, “and we did.”

2001’s Sound-Dust is the final album Hansen played on, and Gane’s favourite along with Cobra and Phases: “I like things that are sprawling and not identified really easily, not easy to digest but there’s a lot of possibilities in them.”

Sadier was inspired by Brazilian modernist architect Oscar Niemayer, a master of harmony and lyricism in concrete. She contrasts his work with a recent drive she took through new-build developments in Newham, east London. “How can you be mentally fit and blossom as a human, and be happy, in this environment? I see it as pure evil, to crush people, to crush their souls.”

Instead, she says, “let’s aim like crazy for the nicest possible thing! Imagine and go for it. Because we can. If you aim at the moon you might hit a star.” In their idealism, beauty, and resistance to capital, Stereolab remain their own little utopia – whether doing it for the money or not.

• Emperor Tomato Ketchup and Dots and Loops are reissued on 13 September by Warp.