Lena Dunham called them “iconic”, Beth Ditto said they “changed my life”. In a decade when alternative music was hijacked by Coldplay and James Blunt, and Green Day’s American Idiot was the closest rock got to social outrage, Sleater-Kinney were a cult force, writing radical anthems of rebellion that tackled issues from gay rights to the War On Terror with a high-kicking bravado that made guitar music feel revolutionary again. But then they stopped. In June 2006, a statement was issued thanking fans, and an “indefinite hiatus” ensued.

Nearly a decade later and the trio are assembled in a hotel room in Newcastle. Tonight, they will play their first show in the UK since 2006 off the back of a triumphant new album, No Cities to Love. The comeback is their eighth record, but it palpitates with the political urgency of their 1995 debut. Price Tag seethes against consumer capitalism, Surface Envy is a battle cry for collective action. But it is also a record about growing older and friendship – its stadium-ready choruses are not ballads of despair, they are songs to rally around. “This band has a weight to it,” says drummer Janet Weiss. “Our songs feel important to play … That was missing in my life without Sleater-Kinney.”

Before their break in 2006, life within the band had become – as each of them will say at least once during our interview – “intense”. “We’d been in a cycle of write, record, tour for 10 straight years,” Janet sighs. “It took its toll, physically, mentally and emotionally.” Singer-guitarist Corin Tucker, who had just had her first child, was finding it impossible to balance the pressures of being a new mother with life on the road; fellow singer-guitarist Carrie Brownstein got sick: “Stress-related illnesses ... I was coming out in hives, having panic attacks,” she recalls.

So they called time. Carrie forged a successful television career – writing and starring in Emmy-nominated comedy sketch show Portlandia with Saturday Night Live’s Fred Armisen. Corin released two, in her own words, “middle-aged mom records”, raised two kids and formed a side project with REM’s Peter Buck and Nirvana’s Krist Novoselic. Janet played in various bands – Stephen Malkmus and the Jicks, the Shins. Put simply, their time was spent doing anything but being in Sleater-Kinney.

In 2012, that changed. Carrie was at Corin’s house, sat on her sofa in Portland, Oregon, watching the episode of Portlandia that her son appeared in. Corin says: “I just wondered aloud, ‘Will we ever play music together again?’ And from then the door was open.”

Ask them whether they ever discussed a reunion before this time and they flatly deny it. But then, discussions about Sleater-Kinney’s internal politics have rarely widened further than the three of them. When a magazine revealed in 1996 that Corin and Carrie had fleetingly dated, they were horrified. The musical chemistry between them – intricate guitar and vocal parts that wind and weave around each other – is one of the band’s defining features. “We’re very close,” says Carrie. “I’ve been friends with Corin for over 20 years. There’s an inevitability to knowing someone for that long…”

“It’s very insular,” Janet attests later on. Spend more than five minutes in a room with Sleater-Kinney and this is evident. They seem to communicate by telekinesis. After each question, their eyes flicker between each other, before one comes forward to answer. That’s not to say they are difficult, or standoffish even. In fact, they’re sharp, smart and funny – steering conversation from Janet’s black nail varnish and Corin’s neon pink jeans to the successes and failures of the Obama administration. It’s more that they are just a bit shy. Strap a guitar around her and Carrie struts around the stage with a Mick Jagger hip swagger, shredding riffs with Pete Townshend arm windmills. Off stage, she cuts a tiny, softly-spoken figure buried so deeply within her scarf that she is barely visible but for two dots for eyes.

“We definitely explore different roles for ourselves on stage,” says Corin. “People might see us playing characters that are ferocious, dangerous and just downright ugly sometimes.”

Corin was 19 when she arrived at liberal arts school Evergreen in Olympia, Washington. The Seattle grunge explosion was just a drive away, and the riot grrrl movement, set up in part as a protest against its macho aggression, felt genuinely revolutionary. Inspired by groups such as Bikini Kill and liberated by pioneer Kathleen Hanna’s “girls to the front” gig policy, Corin put together her own band Heavens To Betsy. The group helped her develop her voice – a holler that sounds an alarm siren against apathy and censorship.

By the time Corin met Carrie in 1995, riot grrrl had dissipated – a demise Corin would later lament in the band’s song #1 Must Have, which hit out at the movement’s ideas selling out and being marketed back to women as “girl power”. But despite remaining vehemently independent (they have consistently rejected any major label offers) the band always had ambitions beyond the underground scene: “You don’t just want to preach to the choir, it doesn’t raise the stakes high enough,” Carrie says sharply. Janet joined the band in 1997 for their third album Dig Me Out. Still their most commercially successful record, it propelled them out of the Olympia DIY scene on to bigger stages and into mainstream consciousness.

“When I started in Sleater-Kinney, I was pretty shy as a performer,” says Carrie, her head now fully visible as the Siberian air-conditioning is fixed and warm air blasts into the room. “I didn’t really do that much in the band beyond play.” As time went on, “I was able to express myself, to get a sense of myself as larger than who I was. From then on, it was a lot of freedom.”

No Cities to Love rings with that stridency. Lyrically, it is not unfamiliar territory for the band, meshing righteous political anger with unsparing self-reflection (“We live on dread” they cry in Bury Our Friends, an unflinching account of contemporary anxiety). But it also sets out their stall as a band. On 2005’s The Woods, they railed against a stagnant contemporary music scene obsessed with black-clad white boys ripping off Joy Division: “You come around looking 1984 / Nostalgia, you’re using it like a whore,” they spat on Entertain. This time, their reflection on music feels more like a plea: “I want an anthem,” reels No Anthems. “A weapon, non violent, a power source.”

The trio return to a very different musical climate from the one they left in 2006. “The idea of the long-haired, white male rocker is moving further into the past,” says Janet.

“It’s great for my daughter to see Beyoncé and Taylor Swift, women that are in charge of their own careers, writing songs from their own perspective and taking people to task,” adds Corin. “That’s very different from when I was growing up – it was all like ‘Stand by your man’.”

“What, Tammy Wynette?” says Carrie. “Hang on … that is waaaaaay ... What are you, like, 60 years old suddenly?” And the three of them descend into laughter. “OK, OK, OK,” says Corin, returning order. “That may be so. But compare them to Britney Spears, who just seemed propped up, you know the pop world seems so different now to then.”

Personally, the band is also in a very different place. Carrie’s filming schedule with Portlandia and Corin’s family commitments mean that the gruelling, 14-month-long tours are logistically impossible. Even if Corin’s husband, the film-maker Lance Bangs, is “hugely supportive” and a “huge Sleater-Kinney fan”. Perhaps, at times, even too much.

“God, he wants to come to every single show,” she groans. “I keep having to ring the kids’ schools and be like, ‘Umm, they’re not going to be in again because they were at another concert.’ My daughter is thrilled. She’d never seen Sleater-Kinney, so I wasn’t sure how exactly that would go over. But the first time she saw us, she actually came up to me afterwards and was like [whispers and gives glaring look], ‘Mom, this is really, really cool.’” And they all fall about laughing.

• Sleater-Kinney are touring the UK, Europe and United States. Details: sleater-kinney.com