ASK Carl Barât whether The Libertines and T in the Park have unfinished business and his reply is unequivocal.

"Absolutely," states the co-founder, co-guitarist, co-writer and co-lead singer of the defining British band of the new millennium.

Ask his partner, Pete Doherty, the same question and the reply is the same, albeit for different reasons. They may be appearing at next weekend's event as triumphant headliners, but The Libertines' one and only previous appearance at Scotland's rock festival was, to say the least, problematic.

Does Barât recall that 2004 show?

"Yeah, I do. Well, I remember various bits of it. I was wasted," he says, wincing slightly. "I remember going out into the crowd for a bit and it was just carnage - people were really intent on having it. That was when our guitarist jumped on [then-Radio 1 DJ] Zane Lowe and just floored him at the start of the interview. Which was really good!" he chirps. "But I loved the vibe. I loved the up-for-it-ness. Scotland's got a reputation for being the place with the best audiences in the world - so imagine that at a festival, at T in the Park. Everyone's just there to do what they love."

Good stuff ... If only Barât was describing the correct show. He's not talking about The Libertines, the rackety, punky, cult foursome founded in London by him and Doherty at the turn of the century. He's referring to a subsequent T appearance with his post-Libertines band, Dirty Pretty Things ...

"Yeah, I'm thinking about the wrong bloody band here!" the 37-year-old exclaims, just a bit embarrassed. "Yeah, 2004, that was a really unpleasant summer for me," he admits with a weary shake of the head. "That's what Peter calls being slung out of the band, and I call finishing our commitments so we didn't get sued."

This exchange tells you something about The Libertines and their storied history. For one thing, the chaos - the indulgence and the partying - didn't end when the band split, after Barât lurched into Dirty Pretty Things and Doherty spun into Babyshambles and an on/off solo career, a relationship with Kate Moss and a period as the nation's favourite rock'n'roll villain. For another, the reverberations of 11 years ago rumble on, still. The Libertines may have, against the odds, reunited to make a new album and, at T in the Park, headline their first ever UK festival. But more than any other contemporary band, their past is always present.

In 2004 the band had just released their second, self-titled album. They had a busy summer of promotional and concert bookings ahead of them. There was only one problem: Doherty, the yin to Barât's yang - the rock to his roll, the Steptoe to his Son - was no longer in the band.

Did he jump or was he pushed? Even now, it's unclear. The Libertines were frenetically, brilliantly chaotic onstage, but catastrophically chaotic offstage. They were infamously bedevilled by internal, often drug-related conflict even before they began work on the follow-up to their influential and generation-defining 2002 debut Up The Bracket. Then, having barely managed to make it to the recording studio together, the Barât/Doherty partnership splintered - seemingly fatally.

The bruising summer of 11 years ago, then, found Barât, bassist John Hassall and drummer Gary Powell forced to tour as The Libertines minus one of their frontmen. Given that the four-piece's appeal was predicated largely on the alchemical magic that occurred between the two singers, this was a heavy blow indeed. The sad thing was, it was hardly news. The Libertines had been forced to tour the previous summer, too, without the errant Doherty.

"I know, I know," Barât acknowledged backstage at T in the Park that July. "Doesn't make it any easier though." By his side, in place of Doherty, was a pair of hefty security guards. In a telling indication of just how toxic things were between the erstwhile brothers-in-arms, the muscle was along for the ride lest Doherty turn up at the festival and cause some trouble.

"Pete's into [playing] festivals," Barât continued, "but he's not very well at the moment. It would be nice to have him here but there's no point in compounding his illness by accepting it."

Asked whether being in The Libertines was bad for Doherty's health, Barât's retort mixed pithiness with hurt. "No, taking smack and crack is bad for his health ... I ain't gonna sack him from the band, I'd never do that. But maybe if he doesn't get better in the foreseeable future I might have to put a lid on it until such time as he does. I'm not gonna keep doing this," he noted, nodding to the bouncers, the T in the Park crowds, the odd circus he was here forced to endure, "forever. I want this record to have the f***ing birth it deserves."

By the end of 2004, their concert contractual obligations fulfilled, The Libertines were, finally, kaput. Surely there was no way back from the depths of such enmity, addiction and bitterness?

And yet ... Summer 2015 finds the four members of The Libertines talking at a pivotal time in their second life. Having reunited for shows at the Reading and Leeds festivals in 2010, then again for a handful of big-ticket gigs last summer, this year they're back once more. But back properly this time. Doherty, Barât, Hassall and Powell have just finished making a new album in Thailand - a location chosen in part because it was where Doherty underwent his most recent, and seemingly most successful, stint in rehab. It was that undertaking to get clean, or at least make a concerted effort to, that was fundamental in persuading all parties to get the gang back together, and get back in the studio.

The band are still finalising various details of a third album due to be released around the time of their second UK festival headline appearances, at Reading/Leeds in late August. But Doherty admits that, lyrically, "there's a lot of stuff been getting off chests. Some of these lyrics have been ... I don't know about cathartic," the 36-year-old says in the hoarse whisper that has long characterised his speaking voice. "But just f***ing ... cruel."

Is it difficult for the pair of old pals, pointed lyricists both, to hear cruel lines from the other one?

"It can be," replies Barât in the speedy mumble that is his speaking style. "It depends how you look at it really."

"Carl wrote a couple of - can I use the word 'couplets?' Will I get stoned in public for using that word," Doherty says with evident sarcasm. "And I actually sing them, so I'll get the glory, and they're an incredible couple of lines. I actually wept. They go: 'In my cinematic mind, I see battles fought at sea/I wake from dawn's empire, it must be lonely being you, being me.'"

Without hearing the rest of the song, it's hard to divine the overall meaning of that lyric. But Barât acknowledges that it references he and Doherty's relationship, albeit (it seems) filtered through their familiar interests in military history, a faith in a mythical Britain they style as Albion and a love of romantic imagery.

Hassall and Powell's views on the Doherty/Barât relationship are instructive. The Libertines' rhythm section have been the steadfast sidemen as the frontmen's on/off bromance has played out around them, and on the front pages of the newspapers. Powell points out the obvious: that before Thailand, the four of them hadn't been in a studio together for over a decade.

"And in that time there's been a lot of changes, to say the least," observes the perennially cheerful drummer with knowing understatement. "Everybody's done lots of different things," the 45-year-old says of intra-band CVs that encompass activities as varied as new bands (Powell was also in Dirty Pretty Things, Hassall formed Yeti), life-threatening, alcohol-induced pancreatitis (Barât), repeat arrests and incarcerations (Doherty), acting roles (Barât appeared on the London stage in Sam Shepard's Fool For Love, Doherty was in arthouse French film Confession Of A Child Of The Century) and the writing of no-holds-barred memoirs (Threepenny Memoir by Barât, From Albion To Shangri-La by Doherty).

"So," continues Powell, "obviously everybody's opinions and viewpoints about recording have changed a lot since we recorded back in the day. But luckily that has only become a positive."

"And the fact that we're 10 years older," chips in the deadpan but friendly Hassall, 34, "and 10 years more experienced, has given a different, much better situation in the studio, and that really shows in the new album."

In terms of Doherty's health, the plan is for his counsellor from the Thai rehab facility to accompany the band this summer on their run of European gig commitments.

"That's helpful for his state of mind," says Powell firmly. "Absolutely. At the moment there's only positives to be taken from this whole experience - and that's irrespective of whether the new record does well or not. The fact is, we formed the band as friends. And that's the least we should be able to take away from this experience. If everybody hates the record I still want to be able to maintain the relationship I have with Carl, John and Pete. I still want my friends. That is the one thing that has been lacking in the past 10 years."

For his part, Barât admits to being pleasantly surprised that, for all the rancour and disarray that attended the band's messy collapse 11 years ago, he and Doherty quickly and naturally resumed their artistic and personal kinship. For The Libertines - and libertines, as they style their shared outlook on life (and they have the matching "libertine" tattoos to prove it) - old bonds die hard.

"When we started [this album] we only had four demos, and some bits. But when we started channelling [the songwriting] it came out so fast, and there was so much of it. We have lots of old songs that no-one's ever heard before that we could have allowed in. But they didn't really make it - we used one and two halves of those songs."

It was important, he says, for him and Doherty's partnership that everything had to feel like a fresh beginning, and renewed. It was also important that this time round they had a recording experience that erased - or, at least, counterbalanced - their memories of making That Difficult Second Album. Then, they were at each other's throats, and required outside assistance to keep the peace in the studio.

"Yeah, we didn't need our own bouncers this time," he observes with more wryness. But just as all concerned are loath to dwell on the past, Barât certainly is trying to take a longer view on the dysfunctionality that characterised The Libertines' first act. "Now, further down the line, looking back, the problems that we had are so easy to diagnose ..."

Doherty, more than anyone, wants to put all those problems, those darknesses, behind him, for obvious reasons. Addiction is an ongoing issue for him, as it is for anyone who's been in rehab; there is no "cure". Accordingly he wants - needs - to focus on the positives. Unlike their brief reunion in 2010, this one feels more solid. More ongoing. It's part of a clean start that began with last summer's well-received shows, kicked off with a rapturous reception from an audience of 65,000 at London's Hyde Park.

"We've had more time together," says Doherty. "In that sense, we were building up to this, where we've been together night and day, and writing together. This is a completely different atmosphere," he concludes with a smile.

So, T in the Park this time round will be completely different, too. A counsellor may be required, but bodyguards shouldn't be.

"No," says Barât, smiling too. "But 2004 was a funny time. So it's great to get to go back and headline. I'm well happy about that."

Against the odds, and against expectations - their own especially - The Libertines are back. With more than a few things to prove at T in the Park, it should be some show next weekend.

The Libertines headline T in the Park on Saturday, July 11. For full line-up and ticket details see www.tinthepark.com