This winter, comedian Ari Eldjárn will play to thousands of people in his home town of Reykjavík. Seventeen shows in nine days in a 1,000-seat venue. It’s an annual tradition for the Icelandic standup, whose easygoing tales and punchy jokes have made him the biggest comedian in the country. But when he performed his first shows in English – two years ago at the Edinburgh fringe – he was delighted when 40 people showed up. “I had no PR, no agent,” says Eldjárn. “I didn’t know whether that was a good crowd or not. It turns out, in Edinburgh, that’s a very decent amount!”

A former flight attendant, Eldjárn started standup a decade ago “as a dare”. Two of his friends gave comedy a shot and, at their second gig, invited their pal to perform too. “There was a huge appetite for comedy in Iceland at the time,” explains the 38-year-old. “I think it had something to do with the fact that the country almost went bankrupt the year before.” Eldjárn soon quit his job as a copywriter to become a full-time comedian with his friends. “We formed a group, and we’ve performed 500 times since then, selling a combined total of 90,000 tickets in 10 years.” For a country with a population of 360,000, that’s mightily impressive.

In Iceland, Eldjárn has had several TV specials, sold out theatres for months on end and performed with the Icelandic National Symphony. “You think: I can’t believe I can do this bit and then introduce a piece by Mozart – and it works,” he says. “I got to conduct the symphony too, which went terribly. I did a long roast about conductors and how they aren’t really doing any work, just waving a stick. Apparently it’s way more complicated.”

A former mayor of Reykjavík was a standup but a comedy “scene” has only really existed for the last few years in Iceland. To be a comedian in a country with such a small population, it pays to be productive. “You really need to turn over material very fast. Especially if you are fairly active on the corporate gig circuit. You will have a lot of people who will see you multiple times that probably didn’t even ask to see you!”

Eldjárn writes a new 80 minutes of material each year for his end-of-year shows. When he translates those jokes into English, ‘“it’s like a rebirth of material”.

At home, Eldjárn’s stories of everyday life in Iceland are observational and relatable. Abroad, that material takes on a new educational form as he explains Icelandic living to foreigners. ‘“But it gets the same reaction – that’s the bizarre thing. You just need one line of backstory or background.”

I had a routine on mindfulness and yoga – in Icelandic it has four killer puns in a row. It was impossible to translate

Anecdotal material is simple to translate. But some routines – especially those with wordplay – require word-by-word micro-translation. And there’s a limit to what can be converted to English. “I had a long routine about mindfulness and yoga, and that’s my favourite bit in Icelandic because it has four killer puns in a row. But it was impossible to translate!”

With so much work and a huge fanbase in Iceland, it must be tempting to never leave home. But Eldjárn says it’s been “incredibly refreshing and a complete adventure” to perform in the UK. “Iceland works as a really good place for me to write and to stay active. But to go to the UK and get a good reception to your stuff – in my mind, that means you’ve made it.”

• Ari Eldjárn: Eagle Fire Iron is at Soho theatre, London, 7-12 October.