In Puerta del Sol square, in the heart of Madrid, a group of pensioners armed with megaphones had gathered to angrily denounce the government's failure to protect their savings. Nearby, past the street hawkers and the tourists, a young man quietly entered the fourth day of a hunger strike.

These two small-scale protests this month show that anger in Spain – at corruption, recession, debt, the lost generation – has scarcely abated since a group calling themselves the "indignados" occupied Puerta del Sol in May 2011. Now, a new political party, Partido X, has emerged from the protests, with the intention of breaking the hegemony of the People's party (PP) and the Spanish Socialist Workers party (PSOE) that have taken turns to run the countryfor the last 30 years.

"In Spain there is a political class that, at best, doesn't understand the needs of civil society, and at worst is completely corrupt and bankrupt. They have to go," said Simona Levi, a theatre director, actor and longtime political activist who has become something of a spokeswoman for the party.

The PP and PSOE have lost millions of voters since the crisis began five years ago, and it is this space that Partido X wants to occupy. The careers of the prime minister, Mariano Rajoy, and the PSOE leader, Alfredo Pérez Rubalcaba, were formed in the 1980s, when the country was firmly divided between left and right. Their rhetoric is that of two old boxers, endlessly trying to knock out their opponent and unaware that many have long since tired of watching them fight.

"They are dead. It's just no one has bothered to give them the death certificate," said Gonzalo Boye, editor of the satirical magazine Mongolia. "Spain is the Titanic and the government is the musical band."

Jorge Arzuaga continues his hunger strike in Plaza del Sol. Madrid. Photograph: Vallejo/Demotix/Corbis

The chief focus of attack is corruption. Listing the number of open investigations into financial and political corruption is almost impossible. At national and regional level, at least 130 politicians of all stripes are facing charges ranging from pillaging state coffers to handing family members plum jobs. But that barely scratches the surface, and is reflected in the social standing of politicians, with poll after poll putting them at the bottom of the ladder.

The hunger striker, Jorge Arzuaga, who was with the indignados at the start of their heady journey, said the venality of the entire political class is the target of his anger. "It is my way of saying I've had enough of this corrupt government. Every day the situation gets worse, and it's time for change," he said.

Partido X is positioning itself as a force for such change. Like many young parties, it is light on policy proposals in some areas, but says it has its sights set on tackling corruption with a "Nuremberg-style trial for bankers" and a dedicated anti-fraud unit, and to bring in more participatory democracy, with regular referendums.

The party promises to provide financial aid for Spain's small businesses, increase the minimum wage and introduce a maximum wage so no boss can earn more than 10 times his or her staff. These, and various other measures, may earn a shake of the head from the financial sector, but could appeal to those who have been left on the margins.

Unlike the traditional parties in Spain, Partido X understands the power of the internet, and its members have been using social media to spread their message and gather funds as well as ideas.

Simona Levi, right, and fellow Partido X member Joaquin Pagola formally unveil the party at a press conference in Madrid. Photograph: Gerard Julien/AFP/Getty Images

The party refuses, however, to be drawn on whether it is of the left or right. It describes itself as "progressive", a rejection of old-style politics. Partido X has not yet committed to putting forward candidates in next year's European elections or Spain's general elections in 2015, but believes it could have millions of supporters by then.

Its aim, said Levi, is not just to get "one poor soul elected in order to send them to Brussels to waste their time". The party hopes for 25% of the vote, which most observers say is fanciful. But with so many disaffected voters, Partido X believes its time has come.

Levi said the party was still in the process of drawing up its programme, but added: "In all elections from now on, the voice of the people will be heard. We are working on our policies, listening to our supporters, and then we will find the right people to stand."

Asked whether the party was Eurosceptic, she said: "We are following our route map, and if Angela Merkel doesn't like what we have to say, that's up to her. Maybe Germany will be the only country left in the euro."

Many have drawn comparisons with the Five Star movement led by the comedian Beppe Grillo, which stormed the Italian elections last year. Levi, who was born in Italy, agrees there are some similarities, and that the two groups have been in contact, but says Partido X is keen to avoid being led by a populist, charismatic leaderand sees itself as a "party of, and for, the citizens of this country".

Partido X may eschew traditional forms of leadership, but Levi is an increasingly recognisable face, and the party has the support of Hervé Falciani, the former HSBC employee who blew the whistle on tax evasion in Switzerland. On board as an adviser is Tarso Genro, the governor of the Brazilian state Rio Grande do Sul and an ally of ex-president Luiz Inácio Lula da Silva.

The sociologist Alejandro Navas, from the University of Navarra, has studied the indignados and understands the appeal in a country where youth unemployment has forced many educated Spaniards to leave. "We tell young people the world is theirs, but then the adult world doesn't allow that to happen. There is a shortage of jobs, and the ones that are out there often have low salaries and short-term contracts."

There is a contradiction inherent in Spain, said Navas: "Young people reject politicians, but they also expect a lot from the state. There is a lot of pessimism and resignation, which it will be hard to break." He is equivocal about whether Partido X can break that mood, and whether its activist base can come to terms with mainstream politics. But, he said, "change will only come from the ground up, from small parties and organisations."