On a freezing winter day last month, a tall man with blond hair walked up to a microphone in northern Moscow and began speaking to 80,000 people. This was not a rock concert or a football match. It was a demonstration against the government – the biggest in Russia since the fall of the Soviet Union in 1991.

The figure marching across the stage was Alexei Navalny, a 35-year-old lawyer. Virtually unknown two years ago, in the past six weeks Navalny has become the talisman of a growing movement for change that has put the Kremlin and Russia's prime minister, Vladimir Putin, on the back foot.

Russians of all backgrounds joined the rally on Sakharov Avenue on 24 December, in protest at the Kremlin "stealing" a parliamentary election for Putin's United Russia party earlier that month. Some waved placards ridiculing Putin's comment that ribbons worn by people at a previous protest looked like condoms. They clapped the speakers, including a former MP in a flat cap like an English country gent – but when Navalny stepped up, a frisson of excitement passed through the crowd.

"I've been reading this little book," cried Navalny, who wore jeans, a black coat and a knotted grey scarf. "It's called the Russian constitution. And it says that the only source of power in Russia is the people. So I don't want to hear those who say we're appealing to the authorities. Who's the power here?" "We are!" the crowd shouted in delight. "Who's the power?" Navalny repeated. "We are!"

This was a sea change. Only a few months earlier, Russia's political opposition appeared limited to a few tortured marginals. Now, for the second time in a month, tens of thousands of students, managers, business owners and shop assistants were joining in one voice to demand their rights. "We've worked so hard to make opposing Putin something cool and normal," said Roman Dobrokhotov, a 28-year-old democracy activist in the crowd that day. "Finally, it's begun."

Navalny, with his youth and good looks, is at the heart of the process. Older oppositionists, such as the former deputy prime minister Boris Nemtsov, are tainted by their brush with power in the 1990s, and don't have Navalny's star wattage among the young. Others are environmentalists or leftist radicals with devoted but small followings.

Navalny's early biography speaks little of the remarkable events to come. His father was an army officer and he grew up in a series of closed military towns around Moscow where he remembers queuing for milk. After studying law at the capital's Peoples' Friendship University, he began to get involved in politics, joining the liberal Yabloko party, only to fall out with its leadership and be ejected in 2007. Next, he co-founded a movement called Narod (The People) and started attending the Russky Marsh, an annual march to promote the rights of ethnic Russians.

Four years ago, Navalny took the fateful step of getting involved in shareholder activism – using small stakes in murky companies to force them to open up their accounts. He started posting investigations into official malfeasance on a LiveJournal account. In a country driven spare by bribery and embezzlement, the blog became immensely popular. One probe claimed executives siphoned off $4bn (£2.6bn) from Transneft, a state-owned pipeline company – a revelation that forced Putin to order an inquiry whose outcome is still pending.

In 2010, Navalny went a step further and recruited a handful of young lawyers to work for a website called RosPil, from the word pilit, meaning to saw off or misappropriate (its symbol is the Russian double-headed eagle clutching two saws in its talons). To date, RosPil has identified violations in £800m-worth of government contracts, many of them apparently inflated tenders designed to put kickbacks into the pockets of bent officials. "Everyone says corruption is everywhere, but for me it seems strange to say that and then not try to put the people guilty of that corruption away," Navalny told the Guardian last year.

"Alexei became so popular because people just couldn't take the government's cheating and lies any more, and they found someone who was willing to do something about it rather than sit and moan in the kitchen," said Vadim Korovin, who runs Net Edru, a website which helps fund RosPil by selling T-shirts and calendars of Navalny dressed as a doctor holding a defibrillator. "He's a man of deeds."

The success of the operation lies in crowdsourcing, rather than an army of workers. Navalny complains to friends about not having an assistant or press secretary. RosPil has only four employees, who work from home, but it invites readers to monitor state tenders published online and to donate to running costs on PayPal. Whistleblowers inside state companies get in touch.

The fervour of Navalny's work is cut with wit. When he described United Russia as "the party of crooks and thieves" last year, it quickly became a meme and is now recognised by two-thirds of Russians. He writes sharp updates on his blog and tweets throughout the day, bantering with 180,000 followers. He and his wife Yulia and their two children are big fans of The Simpsons. As po-faced analysts pondered the opposition's next moves over the new year holidays, Navalny was writing on Twitter: "DO YOU REALLY NOT UNDERSTAND THAT CAPSLOCK IS VERY COOL."

Such playfulness invites scorn as well as affection. When Navalny gave an interview to the liberal Ekho Moskvy radio station last month, the host called him Alyosha, a diminutive of Alexei. Kristina Potupchik, a spokeswoman for the pro-Kremlin Nashi youth movement, pounced. "Imagine for a second that the presenter of the annual phone-in with Putin calls him Vovchik," she wrote.

"Navalny is a colourful personality who makes a lot noise, who attracts attention to himself, but who is totally without substance," said Robert Shlegel, a United Russia MP and former Nashi activist. "He's got no real experience – what, some blogging and a little work as an adviser to a regional governor? No one knows him in the regions. And despite all his bluster, he didn't run to be an MP and he chose not to run for president." Does Navalny pose a threat to Putin's rule? "None at all," Shlegel said.

A poll taken last April indicated 93% of Russians didn't know who Navalny was (although that figure has likely changed significantly since the December protests). Yet if Navalny is really so low on their radar, Putin's allies seem unusually nervous. "I don't like his Führer-style of giving speeches," said Shlegel. "What was he doing, going to Yale University and talking to Tunisians and Egyptians who organised revolutions? Someone pays for such things and they want something in return."

Such slurs are nothing new. Last spring Nikolai Tokarev, the head of Transneft, suggested Navalny was working for the US state department. In November, his email was hacked and more than 1,000 pages of his messages posted online. Then, after the 4 December elections in which United Russia's share of the vote plunged by 15 points, the campaign to discredit Navalny went into overdrive: the next day, he was arrested for allegedly breaking one of Russia's byzantine rules on public gatherings. He and several others spent 15 days in a spetspriyomnik (special detention centre) in southern Moscow.

Putin has never mentioned Navalny by name, but on 15 December he claimed protesters had been paid to attend the first mass rally in Bolotnaya Square 10 days earlier. Then, after Navalny's release from jail, Putin supporters distributed a newspaper in Yekaterinburg which used a crudely faked image to suggest Navalny receives money from the Kremlin's arch-villain, Boris Berezovsky, a self-exiled oligarch who lives in London. And last week, a video appeared on the internet comparing the lawyer to Adolf Hitler.

"Every such step to discredit Navalny will only make him stronger," predicts Stanislav Belkovsky, a political strategist who has known Navalny since 2004. "Navalny is a very serious figure and the most promising politician in Russia today. I'm in favour of him becoming president if the powers of the office are dramatically reduced – but what I'm against is Navalny becoming an object of worship. He should be a member or leader of a team, the first among equals in the European manner, rather than a vozhd (master), in the Asiatic way."

Others also sound this note of caution. Navalny has indicated he will not, or cannot, create a political party until laws on registration are liberalised. He describes himself as a national democrat, but beyond his calls for crushing corruption and bringing honesty to government, his platform is vague.

For now, it may not matter. The paramount struggle is for clean elections and a new framework for political life allowing real competition. The next protest rally is planned for 4 February in central Moscow: Navalny and his allies will urge Russians to vote for any candidate except Putin in Russia's presidential election a month later.

Yet Navalny's more nationalist views are troubling. Last year he spoke at the Russky Marsh, where some protesters made Nazi salutes. He has also endorsed a movement called Enough of Feeding the Caucasus, which protests against the theft of state funding but which critics see as xenophobic. And a video that Navalny recorded for Narod several years ago called for arming the population to shoot Chechen bandits.

"Navalny wants to be a leader, that is clear," said Liliya Shevtsova, a Kremlinologist at the Carnegie Endowment and one of the country's foremost authorities on domestic politics. "The way he has emerged through the internet and social networks, this domain of the younger generation, is very positive. Russia needs new leaders who can break the link with those of the 1990s."

Navalny, she said, "is a chance, a hope. But there is a trap which he may fall into, and that is the search for a new Russian saviour. The people still want a fixer more than they want fixed rules of the game."

Shevtsova believes the lawyer could yet become a destructive force. "We don't know what he thinks strategically," she said. "He seems to have a bouillon of incompatible beliefs because he is a populist and wants to please everybody. In this ideologicial pragmatism, he is no different to another Russian politician: Vladimir Putin."