You may remember Jón Gnarr, the greatest accident in politics. He’s the Icelandic comedian who invented a “joke party” after the financial meltdown of 2008 and won the Reykjavik council elections in 2010. The Best Party – which had no policies to speak of – succeeded the centre-right Independence Party. Gnarr became mayor and the face of Iceland. He’s just finished four years in the job and his time in a suit is done.

I meet him at the Charlotte Street Hotel in London expecting to find an Icelandic Boris or Screaming Lord Sutch. He looks exhausted and speaks slower than any politician I’ve ever heard, pausing for ten seconds to think of his answers. As he orders a ginger beer, I look at the red rims of his eyes and think of a line from his new book, written while in office, recounting his strange story:

Sometimes I am overcome by boundless sadness and despair, and then, much to the displeasure of my staff, I give in to unrestrained self-pity . . . I have the feeling I have gotten myself into something that I will never understand, not even partly. Then I long for my old life.

In Gnarr! How I Became the Mayor of a Large City in Iceland and Changed the World, the chapter called “What You Need to Be a Politician” takes up five pages. Integral to Gnarr’s ethos was the idea that politics is a crap job, just like any other crap job – so we all have the right to become involved just because we feel like it. “We need shy people,” he writes. “We need the overweight, the stutterers and the disabled . . .”

“In Iceland,” he says today, “the image of the right wing was a relaxed, confident and humorous man. Always a man. They have this saying: politics by day, barbecue in the evening. I wanted to break down the image of the confident male figure because it is an absolute illusion.”

Born in Reykjavik in 1967, Gnarr was labelled maladaptio as a child (“a fancy word for retarded”). He did not attend university and worked laying paving slabs and driving cabs, among other things, to finance his stand-up career and support his five children. He had various TV acting jobs: in 2007 he starred in The Night Shift, which made it on to BBC4.

When the banks collapsed at the end of 2008, he started writing a TV sketch show to parody the various political parties clamouring to win the vote after the disgrace of the right wing. Their leader was modelled on Tony Blair, Groucho Marx and an American used-car salesman. His slogans included “Thumbs up!”, “Anything and everything for our underdogs!” and “All kinds of the best of everything!”.

“Here’s how politics works,” Gnarr says. “Men come together and have debates and arguments. And I will try, as one of the men, to say something very clever to another man and he will not know how to retaliate – and I will be the winner of that day. After the meeting, we will all go and drink together and I will be congratulated on the clever thing I said. We will get very drunk and pass out. The next day, we will have a meeting and I will not be well prepared but the other man who was not prepared the day before will be very well prepared. And he will manage to say something very clever about me and he will be the winner of that day. And then we go and drink together and pass out and the next day . . .”

He has a laughing fit, gripping the arm of the sofa.

In January 2009, with the angry populace waging a “saucepan revolution” outside the national parliament, Gnarr decided that his TV sketch might seem a little insensitive, so – and this is the bit I still don’t quite get – he went to the tax office and registered his fictional party for real.

The Best Party called for the opening of Disneyland in Reykjavik, “because the country was awash with people who’d be willing to get into Disney costumes and sell cheap trinkets for a few krónur”. While the Left-Green Movement promised free swimming pool access for children, the Best Party promised free swimming for all – with towel included. It guaranteed a drug-free parliament by 2020. And complimentary plane tickets for women. To challenge anti-immigration views, Gnarr reminded the electorate that the man who brought the toilet to Iceland had been a foreigner: “But it was unlikely that anyone now would be prepared to go without his invention.”

The point, he explained, was that if the party got elected, it would take the job seriously. Real social policy started to take shape: welfare reforms; gay rights; a renewed promotion of Iceland, the only member of Nato without an army, as an international centre of peace. In the 2010 council elections, The Best Party won 34.7 per cent of the vote and six seats on the city council. They joined forces with the Social Democrats, led by Dagur Eggertsson, and Gnarr took his place in the mayor’s office.

He sips his ginger beer and pinches the bridge of his nose. “They asked me, ‘Do you have a suit?’” he recalls. “I said, ‘Yes, I have a suit.’ ‘Do you have a tie?’ I said, ‘Yes, I have a tie, but I don’t wear it because I consider it to be an arrow pointing at your penis.’ Women don’t need to wear ties because they don’t have penises.”

Instead, he got his mother-in-law to paint his nails and would occasionally wear lipstick to meetings. On his first day, he inquired how much holiday he was entitled to. Controversially, when questioned on live TV about policies he wasn’t clear on – which was most of the time – he would admit as much. This annoyed journalists.

“I was frequently pressed to make a quick decision on something I didn’t know anything about,” he says. “ ‘Make up your mind! Make a decision!’ I’d say: ‘But I don’t have all the facts!’ They’d say: ‘Be a man! That’s what women do, discuss things, go back and forth. That’s why they like soap operas, because they never end.’

“We were trying to do a good job,” he continues, “and to show that when it came to politics, just smiling and being happy doesn’t mean that you are not serious. And that is also part of this male act – happiness and laughter is considered feminine. Men don’t do it: we are serious, we are men, look at our eyebrows! It is crucial that we find ways to increase voter turnout and get young people interested in politics. Many people are very reluctant because politics is very boring indeed.”

Does he still think that?

“Yes, it is dull. Very, very dull. But it is also very important. Left-wing issues are in their nature serious and sensitive. Poor people. Sick people. There is a tendency of the left to take oneself too seriously. The sad thing is that the anarchic initiative comes from the right; you can see it in England, France, Holland and Germany. The fascists are funny now. Their YouTube videos make people laugh. It terrifies me. That’s why we decided to do this: we feared that the situation in Iceland might give rise to fascism. We had all the ingredients for it.”

Iceland is now governed by the same right-wing and agrarian-centrist coalition in power when the banks were privatised. The Best Party was dissolved this year; while many members have gone on to join the pro-Europe Bright Future party, Gnarr has retired from politics and is clearly relieved. “The latest poll suggests people in Iceland are losing faith in politics again,” he says. “Trust is going. In the last election, three months ago, it was the lowest turnout ever.”

“Why is that?” I ask him.

“I don’t know,” he says, not atypically. “I honestly just don’t know.”

Jón Gnarr’s “Gnarr! How I Became the Mayor of a Large City in Iceland and Changed the World” is published by Melville House (£16.99)