It is not the sex or sleaze swirling around Silvio Berlusconi that irks Matteo Renzi most. "I checked, and he is only six years younger than my granny," said the leftwing mayor of Florence who, at the tender age of 36, is being tipped as the man to clean up Italy if and when Berlusconi's creaking rule collapses.

As the Italian prime minister, 74, prepares to go on trial on suspicion of paying an underage girl for sex, Renzi is basking in ratings revealing he is the country's most popular mayor. He is now building national backing with a 20-city tour promoting his book calling for a dramatic generational change in Italian politics. Its title? Fuori! (Out!)

"When Italy hosted international summits in 1994, 2001 and 2009, John Major, Tony Blair and Gordon Brown were Britain's prime ministers, but Berlusconi was there every time," Renzi, a member of the centre-left Democratic party, told the Observer. "We need to send a whole generation of politicians into retirement and I am just one of many demanding we turn a page."

Renzi has yet to make the leap to the national stage, but for many it is just a matter of time. In an attempt to drive home his ambitions and youthful credentials, he held a book launch in Florence this month at which he preached change over a U2 soundtrack and prowled the stage before 1,000 fans. It was a far cry from Berlusconi's idea of connecting with young people, which allegedly consists of groping topless girls as they cavort at his private soirées and sending out emissaries to scour beauty contests for a fresh stock of "virgins ready to sacrifice themselves to the dragon", as his wife put it before leaving him.

Last week the allegations of sleaze and debauchery took a dramatic turn in favour of Berlusconi's critics as he was ordered to stand trial, before three female judges, in April. But the media mogul shows no sign of resigning and is beefing up his support in parliament.

Renzi is scathing about Berlusconi's injection of sleazy sexuality into Italian life via his TV channels. "Back in '94, Berlusconi invoked Margaret Thatcher and promised a liberal revolution, but since then it has been a bizarre journey from Thatcher to Nicole Minetti," he said, referring to the showgirl-turned-politician who arranged the parties where Berlusconi met Karima El-Mahroug (also known as Ruby), the Moroccan dancer with whom he is suspected of having sex. "His cultural message is rooted in his sexy 80s shows and he has changed Italy far more with his TV stations than with his laws," Renzi said.

But, despite being increasingly seen as the man with the best chance of toppling Berlusconi, this is about as far as Renzi will go in attacking him. "When Berlusconi wins elections he forms a government, but when the opposition wins we just argue because it is the opposition to Berlusconi that unifies," he said. "I don't know if the Berlusconi era is at an end, but if we spend our time talking about Ruby we are not talking about the Italians," he said. "Has Berlusconi cut taxes? Improved infrastructure, improved life? No, so let's just defeat him with the vote."

Renzi is not embarrassed to say he learned his values at the Florence branch of the cub scouts. He was running the province of Florence at 29 before he ignored his party's advice and stood for mayor of the city in 2009. At the polls he beat off a challenge from Giovanni Galli, a former goalkeeper with Silvio Berlusconi's Milan, who was handpicked by the prime minister to challenge him. After packing the town hall with officials with an average age of 41, half of them women, Renzi is now building an environmental track record by banning building on greenfield sites. His emergence comes as Democratic party leaders squabble over how to knock Berlusconi off his perch.

However, observers say Renzi still has some way to go. One analyst said he was now succeeding in attracting disgruntled Berlusconi voters, but still needed to consolidate his support on the left before he made the switch to national politics.

"If he can use Florence to get a bit more experience, he will be ready. Now is still too soon," said Roberto D'Alimonte, a politics professor at Rome's Luiss university. But Renzi may not have the patience.

"I get nauseous thinking about Italy's political class, which hasn't changed in 30 years, has done nothing to change things and spends its time arguing on talk shows," Renzi said.