Grey clouds hang heavy as the scout troop, a noisy brass band and hundreds of Reykjavik residents, many carrying Iceland's flag, tramp into the cemetery.

A woman in traditional dress lays a large wreath on a grave. It's Independence Day, honouring the 200th anniversary of the birth of Jon Sigurdsson, hero of the struggle for freedom from Danish control.

Overseeing it all is a burly man with a sharp haircut. People greet him, some take their photograph with him. He smiles, then chats to environmental campaigners carrying banners against political corruption.

This is Jon Gnarr, the unlikely mayor of Iceland's capital, who delivered a huge shock to the political system in the wake of the country's financial meltdown.

One year ago the comedian led a gang of ex-punks, poets and pop stars to the control of city hall. They call themselves anarcho-surrealists and their aim is to transform politics.

A stylish blonde in a bright green coat bounds up. Eva Einarsdottir, an activist nicknamed "Palestine Eva", is chairwoman of the national day committee and has come from a ceremony with the President and Prime Minister. How was it? "Fine. I man-aged not to laugh, but it was hard."

Such irreverence has made the Best Party equally loved and loathed. It burst on to the scene before last year's election, satirising politics and confounding traditional parties.

Its first pledge was to break all its promises, making the party almost impossible to attack, then it promised the zoo a polar bear and a drug-free Parliament within 10 years.

The party's only advertisement was in a newspaper personal column, saying: "The Best Party wishes to meet good people aged 18 to 90."

Its 10-point plan had 13 points, and the party's campaign video featured candidates singing Tina Turner's Simply the Best, with the chorus: "We are the best, the bestest of parties, best for Reykjavik, best city of every week." It works in Icelandic.

Iceland was ripe for change, having effectively gone bust thanks to the cronyism of politicians and bankers who wanted to make a financial superpower of an island of fishermen with a population of 318,000.

In less than four years, the most rapid expansion of a banking system in history saw three privatised banks develop assets 10 times the size of the country's GDP. It was the Icarus economy. Property trebled, the stock market multiplied by nine, people borrowed heavily (often in foreign currencies) to catch the boom.

The crash was fast and hard, wors-ened by the collapse of the krona as the state, unable to bail out the banks, refused to pay foreign creditors.

The strategy looks smart now, compared with events in Greece and Ireland, but the country was angry and frightened. Voters wanted change, and the Best Party caught the mood, capturing Reykjavik with 34.7 per cent of the vote.

"No one has to be afraid of the Best Party," said Gnarr in his acceptance speech. "Because it is the best party. If it wasn't, it would be called the Worst Party. We would never work with a party like that."

The tone was jocular, but the intent deadly serious, as becomes clear talking to Gnarr and Einar Orn Benediktsson, who used to sing alongside Bjork in the Sugarcubes and is now Reykjavik's head of culture and tourism. Over dinner, the pair explain their mission to transform political discourse.

"The human spirit has been crushed by small-minded people playing politics," says Einar Orn. "We have no agenda and are just fully engaged in trying to do our best. We have no party members and no idea about spin or political punchlines.

"When we don't know something, we admit ignorance." Given their campaign's frivolity and the fact that the mayor is a famous comedian, best known for playing a bad-tempered Marxist on television, they've surprised people with their seriousness in running the city.

They say their campaign promises had serious undertones - the polar bear pledge was a satirical comment on attitudes to immigration and climate change, since four of the creatures were shot in recent years after swimming into Icelandic waters.

They freely admit they've made mistakes, confronted with huge political problems in a city inhabited by nearly half the Icelandic people.

They had to slash Reykjavik's spending by 10 per cent, cutting bus services and raising charges for services, while Gnarr oversaw the sacking of 70 staff from a mismanaged utility company.

Gnarr has found the role highly stressful, becoming ill as he struggled with complex issues. Speaking at an award to a social worker, he burst into tears, wondering if he was cutting the services that helped him as a teenager. He was relieved he wasn't.

He describes himself as an anarchist, inspired by Gandhi, Tolstoy, Bakunin and the British punk band, Crass. His radio shows have included crank calls to the CIA and the White House, but he claims to have known nothing of politics beyond what he saw on acclaimed TV show The Wire.

"I really like to irritate arrogant people, authoritarian people who want to control what we say and do."

He has banned religious groups from city schools, dressed in drag to mark gay pride and had the city's sky-blue crest tattooed on his forearm.

After his summer holiday, he plans to paint his nails, wear lipstick and campaign for great apes to be given human rights. "I might resign on a really minor issue that I get wrong, since no one here has resigned for all the huge things that went wrong."

Such tactics infuriate the traditional parties, who deride them as jokers and amateurs. "Because of their lack of experience, they have gained power, which is not a good thing," said Kjartan Magnusson of the conservative Independence Party.

"They said they'd never raise taxes which persuaded many people to vote for them, then put them up. They're just another socialist party."

Gnarr was also attacked as a porn user after he got bored with the 400 interviews he'd given since taking office and, asked by a French journalist to name his favourite website, joked it was a porn site.

The emotional, open father of five finds the smears upsetting.

Much of the opposition is in a newspaper edited by David Oddsson, who unleashed the bank boom while Prime Minister.

Best Party tactics are to stay silent under fire, remaining positive and courteous. It's a challenge, admits Gnarr. "But if opponents say 'you're an asshole' I ask them not to state it as fact, but as their opinion."

Now journalists have identified a creed called "Gnarrism", politics by people opposed to politics. And the party is attracting interest around Europe, travelling to Austria, France and Ireland to explain its tactics. Its members' dark humour doesn't always translate: Einar Orn said Irish activists had looked baffled when advised to listen to Lady Gaga.

The Best Party's popularity waned as it tackled tough issues, but still one in five voters back it, with Gnarr viewed as the nation's "most honourable" politician. The question is whether it moves to the national stage next.

Gudfridur Lilja Gretarsdottir, head of the left Green parliamentary group, hopes it does. "We needed something to shake up the system, since it's so corrupt," she said. "Who knows if this experiment will work. But at least there is hope of change in Iceland.

Punk rock to city hall

The son of a policeman and a kitchen worker, the young Jon Gnarr quit school at 13 and joined Reykjavik's punk scene.

At 14, he was sent to a boarding school for troubled teenagers and stayed until he was 16.

During his troubled adolescence he was a heavy glue sniffer.

In Iceland, the sandy-haired 43-year-old is well known for his television role as a character named Georg Bjarnfredarson, an unpleasant, middle-aged, Swedish-educated Marxist whose childhood was wrecked by a militant feminist mother.

As a musician Gnarr travelled with the Sugarcubes, the first band of Iceland's most celebrated pop star, Bjork.