Towards the end of Mark Cavendish's memoir of the years in which he captured cycling's road-race world championship and took his total of Tour de France stage victories to 25, there is a vignette illustrating how close we may have come to seeing a man who took drugs to win the Tour seven times graduate from the top step of the Champs-Élysées podium to the White House. Cavendish's description of his first meeting with Lance Armstrong in 2008 – four years before the American was finally unmasked as a cheat – will strike a chord with anyone who has heard first‑hand accounts of encounters with Bill Clinton.

"There was something mesmeric about Lance," Cavendish writes. "That's something people often say about so-called 'celebrities', but not until I spent an hour or two with Lance did I really fully appreciate what it meant … The energy that he radiated seemed to hang everywhere, yet when he spoke the space suddenly emptied to leave just you and him. His eyes were like strobe lights, burning through you. He inserted your name into every sentence, paid attention to everything you did, remembered everything that you said."

For a year or two, while Armstrong was still bathed in the aura of the man who went from beating cancer to dominating one of the world's toughest sporting events, it looked as though he had set his sights on a political career. If Ronald Reagan could step out of a Hollywood backlot to occupy the Oval Office, then why not a man who had shown, while setting up and heading his Livestrong charity, an ability to command the respect of the highest and mightiest alongside the adoration of multitudes?

Since his spectacular fall, Armstrong has continued to cast a long shadow over a sport whose surge in popularity throughout the English-speaking world has been a feature of the past 20 years, a phenomenon in which he played a leading role. Cavendish, who grew up in awe of his exploits but, like all the products of British Cycling's remarkably successful academy system, emerged from a non-doping culture, expresses his frustration at having his own moments of triumph interrupted by constant questions about the issue in general and Armstrong in particular.

For the record, he favours an approach to the future of the sport based on drawing a line and starting again: reconciliation, if not truth. He is happy to work with several coaches who have acknowledged their drug use as riders during the EPO era but are now, he says, advocates of a clean sport. "These guys all found a way back into professional cycling and, who knows, one day so might Lance," he muses. Interestingly, it was Armstrong who, in 2011, guided him into the arms of a new business manager. But as Cavendish sat in a hotel room in Argentina watching the famous televised confessional to Oprah Winfrey, "the only sympathy I felt was for the sport I love – not Lance Armstrong."

A detailed account of Armstrong's eventual descent into disgrace is given in Wheelmen, the work of two Wall Street Journal reporters who picked up the threads of the story that David Walsh, the Sunday Times sportswriter, had been forced to drop when Armstrong successfully sued his newspaper (Walsh has since been amply vindicated and the money repaid). Reed Albergotti and Vanessa O'Connell cultivated excellent contacts and followed their leads into the boardrooms of corporate America, where Armstrong was a hero. A forceful, charismatic figure, the symbol of a sport supplanting golf as the recreational choice of many young executives, he embodied the take-no-prisoners attitude of turbocapitalism while erecting a facade of compassion and establishing connections with the general public through his charitable efforts, all of which promised to become the platform for a future in politics.

He might have got away with it, had his hubristic insistence on making a comeback in 2009 – four years after his initial retirement – not opened a chink in his hitherto impregnable armour. Wheelmen fills in the details of the tens of millions of dollars that were at stake (and which various bodies are now trying to claw back), while following the journey taken by Travis Tygart, the chief executive of the United States Anti-Doping Agency, a latter-day Eliot Ness who saw through the lies, ignored the threats and maintained the dogged pursuit of his prey.

Cavendish's book is a cheering antidote, even though the Manxman's character is, by his own admission, not one that earns unqualified admiration from all sides. Daniel Friebe, his ghostwriter, catches his voice with great precision as he quarrels with rivals, rages at erring mechanics, grabs a digital recorder from the hand of a journalist who asks a question he dislikes, and confesses that his rift with Team Sky, whom he left after a year, began when he could not persuade his team-mates to remove their used coffee capsules from an automatic espresso machine, thereby offending his compulsive fastidiousness.

The hair-trigger temper – for which he is often equally quick to apologise – can be seen as a major part of what makes him not just a great rider but perhaps the outstanding British international sportsman or woman of his era. The displays of rage are part of the psychological makeup that enables the sprint king to make instant decisions in the crucial last 200 metres of a 200km race, finding gaps where none appeared to exist while extracting the last ounce of power from his legs, using his strength to see off his rivals' attempts at physical intimidation as his brain – which he sharpens via endless games of sudoku and other logic puzzles – whirrs through the finest of calculations in a game of 45mph two-wheeled chess, where errors are rewarded with flayed skin and broken bones.

If he seems – like Sir Alex Ferguson – to need adversaries, whether a troublesome rival or a disobliging reporter, on whom to sharpen his competitive instincts, that is not something that seems to bother the public, who responded to his win in the 2011 world championship by making him the BBC's sports personality of the year. They like to see emotion, something he is richly equipped to provide.

Cavendish is still only 28, but At Speed ends on a note of unfamiliar and rather touching doubt. At this year's Tour de France he was restricted to a mere two stage wins by the German sprinter Marcel Kittel, a young giant who also ended Cavendish's proud run of four consecutive wins in the final stage on the Champs-Élysées. The bitter memory leads him to reflect on the inevitability of one day losing his potency: "It may be that, in the second half of my career, a nemesis comes along to ruin all of my plans and take my records." Could that rider, he wonders, be the young Kittel, a man he actually likes? To be continued.

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