On a rainy night in June last year, 2,000 people crammed into a public school auditorium in Barcelona’s El Raval district. As they waited for the presentation to begin, the buzz was deafening. All of them had come to hear about a new grassroots movement being launched by some of the city’s most prominent activists and academics. “We want to occupy city hall and open it up to the people,” Ada Colau told them as she detailed a “process of revolution and radical democracy” designed to hand back power to the citizens of Barcelona.

One year later, Colau again called on Barcelona residents. This time, though, the setting was city hall. And Colau was no longer an activist aiming to fight power from the outside, but instead the city’s top leader.

“I personally invite you come to the plaza and celebrate our unprecedented collective victory,” she wrote last week on her Facebook account, inviting residents to follow her swearing-in inside city hall from the plaza that sits just outside the emblematic building. “But also because we know that in these next four years, when there are more people pushing from outside, we’ll have more strength on the inside.”

As one of the founders of the anti-eviction group Mortgage Victims’ Platform, Colau has long been a familiar name in Barcelona. In 2013 she became one of the country’s most prominent voices of protest against a political and economic elite who had led the country into crisis when, during a parliamentary hearing on the hundreds of thousands of families who have been evicted from their homes, she pointed to a senior member from the Spanish Banking Association and declared: “This man is a criminal and should be treated as such.” Months later, she was captured on camera being hauled away by police as she and other housing activists occupied a bank to demand that it negotiate with a man who was unable to pay his mortgage.

On Saturday, Colau, 41, was sworn in as the mayor of Barcelona. “It’s a victory of David over Goliath,” said a tearful Colau last month as news broke that her party, Barcelona en Comú, had earned the most votes in this city of 1.6 million people. Crowdfunded and guided by a collaborative platform that features input from more than 5,000 citizens, the leftwing coalition – backed by Podemos – earned 11 seats in the 41-seat assembly. “This victory is thanks to the hard work of the thousands of people who’ve shown politics can be done differently,” said Colau.

She and her team will now push forward with what they call their emergency plan; a list of 30 measures aimed at creating jobs and fighting against job insecurity, guaranteeing basic rights and tackling corruption. Her salary as mayor will be slashed from €140,000 to around €35,000 a year, privileges such as official cars will be a thing of the past and bankers will be hauled into meetings to discuss how to halt evictions and turn the empty homes on their books into affordable housing.

Leftwing parties with roots in Spain’s indignado movement now govern four of the five biggest cities in Spain; including Ahora Madrid and mayor Manuela Carmena in Madrid, as well as in Compromís in Valencia and Zaragoza en Común in Zaragoza. In Cádiz, A Coruña and Santiago de Compostela, leftwing coalitions that include Podemos are also set to govern.

A tough road lies ahead for Colau –not only because her party, 10 seats short of a majority, will need to constantly form alliances to govern. As her party hands back the reins of the city to its residents and touts a new, participatory way of doing politics, it faces opposition from some who are deeply opposed to the idea.

“I don’t think the ideas of a city can be based on what a citizen’s assembly wants – it’s absurd,” said Francesc de Carreras, a constitutional law professor at the Autonomous University of Barcelona. “Democracy doesn’t mean that everyone expresses their desires and they come true by some miracle.

“It’s not a good idea to have citizens participate in these things. We’re not the ones who have skills in these areas,” he said. “I don’t go into a restaurant and tell them how to cook.”

Others say that Colau’s main challenge will come from inheriting a city at a crossroads. “The Barcelona model is in decline,” said journalist Marta Monedero, referring to the ideas that guided the city’s growth in the late 1980s and early 1990s and helped put Barcelona on the world map. “The model was a way to understand the city and bring it closer to the people – there wasn’t a lot of money so they came up with things like having lots of squares and intensifying the social fabric of the city through organisations.”

Monedero recently co-edited a book called The Dream of Barcelona: A City in Which to Live or to See?, in which she and journalist Núria Cuadrado asked residents from various sectors of society about the issues facing the city. What they found was that the model that had once been so successful in guiding the city was now deeply out of sync with everyday reality. Unlike in the late 1980s, today around 17% of the city’s population is foreign born. Housing activists say that some 15 residents a day were evicted from their homes in 2014. Like other cities across Spain, unemployment remains stubbornly in double digits, while the young and educated continue to leave the city in hopes of finding work abroad.

The failure of policymakers to address these issues has created a climate of inequality that colours ordinary life in Barcelona, said Monedero. “Not just inequality between neighbourhoods, but also between residents and the tourists that come here.” The result is a city that has reached a tipping point, she said. “Barcelona is a liveable city right now, but could stop being that way if measures aren’t taken to correct these differences.”

Colau said during the campaign that inequality is one of Barcelona’s biggest problems. “In the past four years the difference between the most rich and more poor of the city has increased by 40%,” she said, pointing to neighbourhoods where the average income has increased six-fold, while other areas struggle with unemployment, home evictions and families who can’t afford their electricity bills. “An unequal city is a city that can be broken easily, it’s an insecure city.”

Another issue on Colau’s radar is tourism. Recent years have seen the number of tourists in Barcelona more than quadruple, from 1.7 million in 1990 to 7.5 million in 2013. This city is now the third most visited in Europe, with the annual number of tourists outnumbering residents four times over. For many years, these numbers were seen as a success story; with visitors leaving behind more than €12bn a year in the city and supporting an estimated 100,000 jobs.

Tourists in Park Guell – Barcelona is Europe’s third most-visited city. Photograph: Alamy

But persistent issues with noise, illegal tourist flats and rising real estate prices have led weary residents to draw battle lines in recent years against the seemingly never-ending tide of camera-toting, beer-swilling visitors.

In Plaça del Sol, in the district of Gràcia, construction workers hammer away inside a three-storey concrete building, slowly turning it into a 14-room hotel with a restaurant and a pool. In February, after several hundred people attended a protest against the construction of new hotels in the district, the soon-to-be hotel was occupied by activists, who turned it into a impromptu office to help those on the verge of being evicted from their homes.

The group was dislodged by police earlier this month. The words “Gràcia is not for sale” scrawled on the side of the building are now the only remnants of their three-month occupation to protest against the effects of rampant tourism on the city.

Colau has vowed to put a moratorium on new licences for hotel and tourist apartments, in order to take stock of how many there are and how many each neighbourhood can realistically support. The hope, she said, is to avoid Barcelona “ending up like Venice” – a city where locals have been pushed out by tourists.

The city’s most central neighbourhoods have become overrun with hotels and illegal tourist lets, she said, leading to a spike in rents and the feeling among residents that they’re being expelled from their homes. Left unchecked, Colau said, mass tourism in Barcelona could kill off the very essence of the city that attracted the tourists in the first place. “More and more tourists are disappointed when they visit Barcelona because in the centre of Barcelona they find a theme park. Everyone wants to see the real city, but if the centre fills up with multinationals and big stores that you can find in any other city, it doesn’t work.”

Her goal is to distribute tourists across the city and crack down on the precarious, low-paying jobs that often proliferate in the industry. “We’re saying that we need to put conditions on the industry, such as restaurants and hotels, so that they better distribute the wealth.” The tourist tax, which currently is used for tourism promotion, will instead be directed towards providing basic services for the neighbourhoods most affected by the influx of visitors.

Film-maker Eduardo Chibás, who captured the city’s polarised conversation about tourism in his documentary Bye Bye Barcelona, doubted whether moving tourists to other neighbourhoods would help address the problem. “It’s just going to take the problems elsewhere,” he said, pointing to the series of protests sparked in La Barceloneta district last summer, after three naked Italians frolicked through the neighbourhood one Friday morning.

“Imagine the people that live there. They just exploded. La Barceloneta used to be a really nice place to walk around and to be with your family, and eat or have a drink. Now it’s become something very awkward.”

He argued that tourists will inevitably end up drawn to the same areas. “Tourists obviously go to the same places – that’s what they’re here for,” he said, pointing to the masses that throng daily around Antoni Gaudí’s most famous work near his home in the Sagrada Familia neighbourhood. “It’s spectacular. Just incredible,” he said. “One has to laugh at it, I’m not going to get bitter anymore.”

The simpler solution, he said, lies in trying not to have as many tourists in Barcelona. Limits could be put on cruise ship tourists coming into the city, he said, while a crackdown on the thousands of tourist lets that aren’t legally registered with local authorities would help. “If they found a great way of attracting people, I’m sure they can find a way of de-attracting them.”