Think Wales are doing well? Iceland has the most fans per population in Europe - and now they are playing with the big boys.

Magnus Magnusson woke up in Reykavik on Monday morning wondering if it had all been a dream.

The Icelander had seen his country qualify for a major championship for the first time the night before with a tense draw against Kazakhstan. Afterwards the ecstatic players celebrated alongside fans in the city’s downtown bars.

“It took some time to sink in,” said Magnusson, Iceland’s leading football agent, “but it was true. We’re going to France.”

Wales’s success in coming close to reaching their first international tournament since 1958 is rightly being heralded. With a population of three million, the unbeaten Welsh lead group B ahead of Belgium, Israel and Bosnia and Herzegovina.

The achievement of Iceland is even more impressive. The country with a population a tenth the size of Wales, just 326,000, heads a very strong group featuring Holland, whom they beat away last week, the Czech Republic and Turkey. Latvia and Kazakhstan, meanwhile, are not group whipping boys like Andorra are in Wales’ group.

Iceland have shot up FIFA’s World rankings since the 2010 appointment of Lars Lagerback, who’d led his country Sweden to five successive major tournaments. Then ranked lower than Liechtenstein, they’re now 23rd above some very big names in world football. Lagerback’s ably assisted by joint manager Heimir Hallgrimsson, an experienced dentist who lives on a tiny north Atlantic island. No, not Iceland.

Iceland’s success – also nearly qualifying for the 2014 World Cup - comes despite their domestic league being played in the summer because of the inhospitable climate on the windswept, volcanic island touching the Arctic Circle.

Not usually considered a football nation, the game is nevertheless big in Iceland. Average crowds in the top Urvalsdeild division may be only 1,000 but that means a higher percentage of the country’s population goes to football matches than anywhere in the world.

Iceland’s Manchester United supporters’ club alone has 3,000 paid up members, 1% of the entire population. Liverpool are not far behind with 2,200 and those fans of both clubs not on the three hour flight to Manchester, will watch Saturday’s game between the two north west giants in a large Reykjavik pub called Spot. Football conversation in Spot tends to focus on the achievements of the Premier League teams – until now.

Over 3,000 fans travelled to last week’s game in Holland to witness perhaps the best moment in Icelandic international football history so far.

“Winning in the Netherlands was amazing,” said Magnusson. “A draw would have been enough, but to win against a very arrogant football nation – to beat them twice without conceding a goal …”

Most of Iceland’s national team don’t play in the country where they were born and raised. The finest, those who pushed Iceland to a 2014 World Cup play-off against Croatia and who beat Holland twice, play in Britain, Spain, Holland or the top leagues in Scandinavia. Gylfi Sigurdsson is the stand-out in a team of non-stars; veteran Eidur Gudjohnson, 37, is back in the fold and has featured in two of their eight group games.

Iceland’s rise is down to several factors.

It needed to overcome the perennial problems of wind ruining games, of frozen pitches and freezing temperatures. Nine ‘football houses’ - huge indoor halls, arched like Victorian rail stations and often the most imposing buildings in the community, have been built since 2000. Most of them are in and around Reykjavik, the main centre of population and home to 80% of the country’s football clubs. Some are heated, the biggest have stands with seats for 1,800 fans. They’re used year round from 6am until 11pm and have been complemented by a further 20 artificial pitches – even the smallest villages have them.

“The current national team are the first generation who could train all year round,” explains Bjarki Gunnlaugsson, who counts three years at Preston North End among his 14 former clubs. “When I played, you couldn’t train properly in winter. You could run and do weights, but not practice technique, passing or drills.”

Gunnlaugsson’s international experiences were generally negative.

“I played 27 times for the national team and we used to lose every game,” he said. “It was an amateurish environment and we knew we’d lose before the game. Home matches would get 4,000 (at the still unwelcoming Laugaerdalsvollur National Stadium, with two stands and a running track) and everyone would cheer if we got a draw. Now, the mentality is completely different and they’re not afraid of anyone.

“We have a core of quick players who were born between 1988-90. They’ve played together with the national team since 16 and they’re used to success and winning is a nice drug to have. When they were under 21s, they beat the Germany of Kroos and Hummels 4-1. They also reached the 2011 European finals and beat the hosts Denmark 3-1.”

Iceland’s under 19 team doesn’t do as well because many of them are in academies around the world and not playing first team football, but the under 17s team reached the European finals in 2013.

Traditionally, the best young Icelandic players couldn’t move abroad because of work permit issues, but regulations have been relaxed in several countries.

Magnusson, the agent, moved to Holland to be closer to the rest of the football world and his players. Other Icelandics are in football roles around the world. Gretar Steinsson is technical director of Fleetwood Town, Runar Kristinsson, head coach of Lilleström SK in Norway, Olafur Kristjansson, head coach of FC Nordsjælland in Denmark.

“Hopefully we’ll soon see Icelandic coaches in Belgium, Germany and Holland,” says Magnusson, who also looks after the Iceland-raised USA international Aron Johannsson, now at Werder Bremen.

“Icelandic people adapt because they’ve historically had to move abroad. They’re not the most gifted natural talents, but the attitude of the boys is excellent. They speak English, they are independent, they are team players.”

The unassuming Lagerbeck is still picking from a small pool of 21,508 registered players. Holland, whom they beat twice, have over a million.

Iceland have been fortunate. Playing Holland weeks after they’d appointed a new manager helped, while Turkey continue to underwhelm on the international stage, but nothing should detract from their achievement.

A new national stadium is a priority, but for now Reykjavik is a happy place – as Iceland’s basketball team has also reached the European finals for the first time.