A morning with David Millar is like no other interview in sport. Time reels past in a vivid blur of words for this is a conversation fuelled less by the cups of coffee lining the table in a cafe on High Street Kensington than by a tumultuous year in professional cycling. Of course, with Millar, the tangled mess of corruption and courage is best approached via circuitous and sometimes strikingly beautiful routes.

In his elusive accent, echoing all the places he has lived in the world, the 35-year-old Scot talks about writing books and riding bikes, about growing old and inevitable endings, about the familiar rhythms of the seasons and the sharp surprises of fatherhood. But his conversation is bolted down by riveting insights into a damaged sport that could only come from an insider.

Millar sometimes sounds trapped inside the dark maze of cycling. Yet his penetrating gaze as a former doper turned patron of the peloton keeps turning, as if on a rooted plinth, while Millar explains the past, reveals the present and anticipates the future of cycling with a mix of foreboding and relish. Confronting the certainty that new storms are about to break, his words frame the collapse of a diseased old regime.

"It's gone beyond some guys cheating and taking drugs," Millar says of cycling's ongoing crisis. "Cycling has been exposed as a fraudulent sport. It was, until recently, a deeply criminal business. We're facing the darkness of that period, and it is so necessary. This is the only way that cycling is going to climb out of the abyss – by confronting the past just as we have cleaned up the current state of the sport. It has to be done and that's why the UCI needs to take responsibility now."

Millar takes another sip of cold coffee and thinks hard about the coming days. "The UCI need to be very careful," he says, "because the momentum is rolling too fast for them to control it. Just as with Lance Armstrong, we'll reach another tipping point soon. I sense the same looming crash with the UCI – unless they act decisively.

"I don't think they realise what everyone needs is immediate action. They're trying to go through the usual sports-politics way of trying to ride this out until people forget about it. These are career sports-politicians. But they cannot evade this any longer. They have to act quickly or they're going to face a total revolt and they'll be out anyway."

Millar has long led the call for Hein Verbruggen to step down from his tainted role as honorary president of the UCI. But he now turns his scrutiny on to Pat McQuaid – who succeeded Verbruggen as president in 2006. "Pat has to show volition to change the UCI. I've said to him before that the first step is to show complete recognition of the past and assume responsibility for it. But, with the UCI, there still seems to be a sense of denial and an 'us and them' approach. They still claim that they did everything they could to stop doping. Well, they didn't – that's obvious to everyone.

"The more people get educated about the past the more precarious the UCI's position becomes. Within the sport, we had in-depth knowledge of cheating. Now there is a public awakening and the UCI will be in real trouble unless they make a full apology. There seems to be some unbreakable alliance between McQuaid and Verbruggen. Pat needs to cut that cord and move forward. He needs to wake up to the fact that some revolutions become unstoppable."

On the outside, the latest conflict between harassed administrators and anti-doping campaigners might seem just another bewildering spat. But Millar points to the legal wrangle between the UCI and Paul Kimmage, the renowned anti-doping journalist, as another potential tipping point. The roots of this story run deep for McQuaid and Kimmage knew each other for decades in Ireland. McQuaid said recently: "I've known Paul since he was in his pram. I managed his amateur career."

And yet, to the disbelief of anyone who has a passing acquaintance with the depth of Kimmage's resolve in uncovering the truth about doping, McQuaid and the UCI chose to sue him. McQuaid used the word "scumbags" to describe former cyclists who testified against Armstrong and then said he would not allow Kimmage to call him and the UCI "corrupt". A furious reaction was unleashed on Twitter and, on 26 October, the Paul Kimmage Defence Fund sailed past $86,000 (£54,000). Coincidentally or not, the UCI "suspended" its legal action that same day.

Kimmage responded on Twitter "How do I feel? I feel like Maximus as he prepared for battle." His next tweet was even pithier: "On my signal, unleash hell."

Millar rocks with mirth. "That was pure Kimmage. But the bottom line is this: don't piss off Paul. So Verbruggen and McQuaid made a huge mistake. It says so much about them. When I heard about their legal action I wanted to say: 'You do realise this is Paul Kimmage?' I'm incredulous that Pat and Hein could be stupid enough to go after him. He'll literally hunt them down. Don't fuck with fanatics."

He says that last loaded word gently; for Millar understands how the commitment of Kimmage and David Walsh, who stood up to Armstrong, is fuelled by terrible pain and injustice. "The sport has made Paul a fanatic because it absolutely vilified him. Paul loves cycling. He grew up with the sport but it burned him so badly. He was ostracised and got treated like a cunt by so many people – me included – for 20 years. Now all this stuff about Armstrong came out and, suddenly, he was right all along. He's right to still be angry. I'm not sure it's good for him but maybe Paul will be the one to make a difference with the UCI. And here's the beautiful irony. That fanatical voice has been the voice of reason through all this."

What did Millar think when, last Thursday, Kimmage announced he was suing the UCI? Millar laughs: "I thought, 'Brilliant. Good old Paul.' The moment McQuaid and Verbruggen sued Paul they were unleashing the dogs of hell on themselves. They then suspend their case against Paul? Another mistake. Suspending the case looks hesitant and weak again. This could be another tipping point for the UCI because Paul's going to come at them now – no holds barred. Verbruggen and McQuaid could fall."

Armstrong has already fallen by finally conceding defeat after Usada's devastating account of his cheating. "I don't think any of us expected the rapidity of his downfall," Millar says, "just the sheer speed and how hard he has fallen. The revelations have been shocking to the public and his fans – but in cycling what has been shocking is that, 'Wow, he's been caught.' Most of us thought, 'Oh, well, it's Lance, he's gonna get away with it.' We've learned to change the sport from within, and make it better. But we always thought we'd have to live with this elephant in the room – Armstrong and the past. Although it is detrimental to young riders, who don't deserve to be tainted by the past, we need these investigations for the sport to survive."

How will it end for Armstrong? "The optimist in me hopes he'll come out and tell the truth. But it's not so simple now. I think that, behind the scenes, he will be striking deals. Lance has to move forward with his life because he's still a father and a husband and a leader of a charity. So he has to face the truth. The moment he tells his story it will add to the tapestry of that period and stop it being just the Armstrong era. But the longer he waits the more it'll ruin him."

Alberto Contador and Miguel Indurain have recently, and bizarrely, defended Armstrong. "I've thought a lot about them", Millar says of the former Tour de France winners, "because I know Contador and Indurain. I was so disappointed when I read those comments. But I live in Spain and have lots of Spanish friends. Our Anglo-Saxon mentality is puritanical – 'Punish 'em forever, they did wrong.' But the Spanish say: 'He's a father of five, he works for charity, he rides a bike … let's move on.' It was incredibly inappropriate what they said and, believe me, they went 'Oh shit!' when it broke. But they had no idea that what they said was wrong because their mentality is so different."

Bradley Wiggins, in contrast, had spoken out against doping for years. And yet his glorious 2012 has been undermined by criticism that, since winning the Tour, he has not been vocal enough. Millar provides a staunch defence. "Why the fuck should Brad be empathetic to the critics. He spent most of his career thinking that winning the Tour de France was a dream that would never happen because you have to dope. And then the last four years the sport has changed. Basically he got to where he is now through hard work and sacrifice. So when he wins the Tour and people doubt him? No wonder he's angry. He's thinking: 'Fuck you – you haven't worked like I did. How dare you be on your phone in a café critiquing me?'

"Brad had every right to lash out. It's what any clean guy would do. I'm different. I made mistakes. I doped. I cheated. I have an obligation to be vocal and transparent. But I honestly don't think it's the duty of the clean guys."

The toll of an incredible year on Wiggins is already apparent. Last month he suggested he is unlikely to pursue the 2013 Tour and, instead, will target the Giro d'Italia. "It's sensible," Millar says. "The work he put into this year's Tour was incredible. The only way you dedicate yourself with that drive is by doing it once. The stars aligned. Contador wasn't there, the course was perfect, his team was incredibly strong and Brad was on fire. Why would he want to go through that again? He would love a pink jersey [for winning the Giro] on his wall next to the yellow one. He's already got one yellow. Why would he want seven?"

Considering next year's Tour, Millar offers an intriguing insight. "I don't think anyone can beat Contador. He's just so good. But Chris Froome is the only guy Contador is scared of. I've spoken to Contador about it and that's good because he's never been scared of anyone. He watched Chris climb at the Tour and you saw how hard Contador raced from the start at the Vuelta [Tour of Spain]. He was racing to get rid of Chris because he was scared of him. That's going to make it a great race.

"Chris is old-school. He's a quirky, brilliant, eccentric character and I love him. He's got a heart of gold but he's also got a mean streak. With Sky around him, Chris could challenge Contador for real. I think they'll put so much work into Chris, like with Brad, and it's just unfortunate they're having to weather this Armstrong storm because they're losing momentum and energy. But [Dave] Brailsford will fix it. And thank God we've got Froome and Sky because it'll make the race interesting.

"There's still a sad irony here. Sky won the Tour clean and they have become another flag-bearer for the future. But they're getting vilified because their zero-tolerance policy has been questioned. Yet they were still clean. They never doped. There's room for Sky's zero-tolerance aim but there should be flexibility. Teams like ours [Garmin-Sharp – which Millar leads alongside Jonathan Vaughters, his team manager and another former drug-using cyclist turned redoubtable anti-doping campaigner] work by including those of us who made past mistakes."

Vaughters rode with Armstrong and his evidence, alongside that of other former team-mates such as Tyler Hamilton, helped Usada expose "the most sophisticated and successful doping programme that sport has ever seen". Millar and Vaughters have been working against drugs a long time and, while stressing the need to address the past, there is exasperation that the sport's changed culture has been overshadowed.

"Doping is just a non-subject to the young guys," Millar says. "To them it's the dark ages of the sport. It's easy to forget that, when I turned pro, it was everywhere. That's what we mustn't forget. Jonathan and I have this sense of history but we want to change things in the future. We think it carries so much more weight and power to work with people who have learnt from the past and want to make a difference. But it's also easy for others to move away from the fact that we cleaned up the sport – from the ground. You can win the biggest races clean now and that's a seismic change.

"Tyler doesn't know what the sport is like today. He hasn't spent time with us and seen what we've done to clean up their mess. I think it's great what Tyler has done, with the book, and coming to terms with the past. But can we put it into context please? It's such a shame Sky and us are talking points because we're both clean teams and putting ourselves on a soap box in different ways. We both want to acknowledge the past by cleaning up the present and creating a better future for cycling."

It seemed especially moving when Millar won a stage of the Tour this year on a July day which marked the 45th anniversary of Tom Simpson's drug-fuelled death on Mont Ventoux. The past, present and future wrapped around a deeply personal moment. "Once I was over the line I found a spot where I could just lie down and look up at the clouds and feel happy for a few minutes. I knew that the poignant connection with Tom Simpson gave me the chance to be sanctimonious and on my soap box in all my post-race interviews. It was perfect to have the link. Instead of just jumping into it and being holier than thou I could use the past to talk about the present."

This Friday, the day after he returns to Spain, Millar will climb on his training bike for the first time in five weeks. Seventeen years have passed since he first started racing. Yet Millar will rekindle "the slow-burning fire" that should carry him through at least another two years of competitive cycling while, simultaneously, pointing a new way forward for a sport that still consumes him. His reflective yet animated mind keeps whirring even as we say goodbye.

"Maybe next year it will be important for Brad to assume a new role," he suggests. "He will have had time to come to terms with what he has achieved. It would be good for him to take the patron role. And it would be good for Sky. Our two teams could send a really powerful message because, beyond the UCI, we need to be proactive and make people believe in us. That's the responsibility of all who want the sport to continue. We can't let anyone else take the lead. It's up to us to make people believe."