He was one of the best-known figures of La Movida Madrileña, the counter-cultural movement that swept Spain after the death of President Francisco Franco, his lens capturing the transformation of Spanish society as it shed the shackles of nearly 40 years of dictatorship.

More than three decades later, filmmaker Pedro Almodóvar believes Spain is again on the cusp of transformation. “We broke down barriers with the sudden explosion in 2011 of the 15-M movement [the grassroots protests that saw thousands occupy the main squares in Spanish cities] and since then we have been pushing the boundaries for change,” the director wrote recently in an open letter signed by 120 leading cultural figures in Spain.

Pointing to the recent electoral victories of Ahora Madrid (Now Madrid) and Barcelona en Comú (Barcelona In Common) – the two new political movements that won power in Spain’s largest cities in mayoral elections earlier this year – the letter suggests they are about a different way of doing politics. Instead of representing one political party, Manuela Carmena, in Madrid, and Ada Colau, in Barcelona, front citizen platforms made up of individuals from a wide range of leftist parties, social activists and thousands of citizens with no political affiliation.

United by a desire to return politics to ordinary people, these platforms managed to seize power in cities from northern La Coruña to Cádiz at the southern tip, moving the protesters – known as the indignados (the outraged) – from Spanish squares into the halls of power in more than half a dozen cities across the country.

Now the push is on to bring the same sort of political transformation to the highest level of Spanish government. A citizens’ platform launched this month and backed by thousands of Spaniards aims to create a national version of these broad, leftist municipal movements. The name given to the initiative, Ahora en Común (Now in Common), is a nod to this inspiration, merging the names of the citizen platforms that triumphed across the country last May.

“This was born out of a clamour from the streets,” said Joan Albert Fabra-Barrios, one of the 200 or so people behind the initiative. He contrasted the victories of the platforms in the municipal elections with the regional elections, where leftist parties such as Podemos chose to run on their own and came third or fourth. “We think that Podemos will fall short if it goes at it alone. Many of us who participated in these leftist coalitions during the municipal elections thought this model would be the best way to win the November general elections,” he said.

Since the launch of Ahora en Común this month, more than 26,000 people have signed up. While many have ties to leftist political parties or activist groups, a significant number have no political affiliation at all.

The project picked up pace a week after its launch when Almodóvar and other cultural figures published their open letter urging Spanish leftists to come together to support the project. “The regional and municipal elections showed us the road to follow to get rid of [the prime minister] Rajoy, bipartisanship and austerity measures,” they wrote. “We can’t allow another four years of evictions, insecurity and inequality.”

As the platform gains in numbers, many in the Spanish media have framed the new initiative as a direct competitor to Podemos. But that is far from the intention, said Fabra-Barrios. “Podemos was born out of a spirit of coming together for change, but they’re asking everyone to unite under their banner,” said the 18-year-old student from Molins de Rei, near Barcelona. “There are a lot of people who don’t want to give up their own projects just to fit into someone else’s. Our call is much broader.”

Ultimately Fabra-Barrios and many others behind the new initiative hope that enough Spaniards will sign up to convince Podemos to also join the movement, much like what happened with Ahora Madrid and Barcelona en Comú.

“It’s not our intention to divide the left. On the contrary, we want to open this space for people who don’t feel represented by specific political parties.”

Since the launch of Ahora en Común, Podemos’s leader, Pablo Iglesias, has repeatedly said his party has no plans to join forces with the platform. “We’re not going to allow ourselves to be led into a space in which winning the elections would be impossible,” he said this month. When asked about the many Podemos members and supporters who have signed up to the initiative, Iglesias said he had “maximum respect” for their position. In recent days his position has softened: he said Podemos members will be consulted on whether to join forces with Ahora en Común.

For some, Ahora en Común’s creation was caused by the shortcomings of Podemos, said Barcelona writer and filmmaker Arianne Sved. Explaining her decision to join the initiative, she said: “For me, there is a disappointment in the way that things have evolved in Podemos and how it has seemed to close up.”

She pointed to the polling numbers for Podemos, which have put the party in a virtual deadlock with the conservative People’s party and opposition Socialists, raising doubts as to whether Podemos will actually be able to do away with the bipartisan system that has governed Spain since the death of Franco.

“The feeling of a lot of people is that Podemos has reached a limit, and with only Podemos we’re not going to be able to win the election,” she said. “Podemos was a big innovation in Spanish politics. The municipal candidacies went one step further. So we thought, let’s do the same.”

Ahora en Común is in its early stages, she said, and is now calling on Spaniards to sign up and get involved in shaping the initiative. “At the moment, there is a lot of potential. We’re not properly organised, it’s a little bit chaotic – but we’ll sort it out.”

For Spanish leftists, launching a united front for the general elections seems like the next logical step, said David García, a 28-year-old teacher from Madrid. “Ever since the indignado movement, there has been a growing culture of citizen empowerment, of citizen participation in politics. Ordinary people feel that they are writing history and that they can change things through collective action.” “This doesn’t imply a critique to anybody, it is an invitation to build together something bigger, something more powerful.”

This emerging political model has, he added, created a culture of hope as the country struggles to recover from the economic crisis. “A country like Spain, that was depressed and in the midst of a crisis, is now thriving with political innovation. It’s all made from below, by regular people.”

Along with winning the year’s general elections, Ahora en Común hopes also to carve out a path that could be followed in countries across Europe. “We’re transcending the limitations of the representative democracy through trial and error,” said García. “And we’re rewriting the old politics of Europe.”