In a dimly-lit, wood-lined bar-restaurant, Burns Night is in full swing.

Haggis and whisky are on the menu, there's Irn Bru behind the bar, and the kilt-clad staff more than look the part. In a corner lined with tat-shop Saltire bunting, a band plays My Love Is Like A Red, Red Rose, while on the tables Oor Wullie grins cheekily on little tartan flags. Watching over all this is the bard himself, his heroic head-and-shoulders visage captured in an image made iconic by Alexander Nasmyth's 1787 portrait, and made immortal on shortbread tins for ever after.

Look closer, however, and you notice that Nasmyth's image of Burns has been altered so that he now seems to be sporting a Nordic woolly jumper, while a volcano appears to be erupting out of his head. The band, meanwhile, made up of an ad hoc supergroup from Edinburgh's lo-fi DIY music scene, has somehow conspired to imbue classics from the Scots canon with a drone-based urgency more akin to The Velvet Underground than a regular Burns Night turn.

Outside, the blanket of thick white snow is a bracing reminder that this Burns Night is actually taking place, not in some Highland village hall, but in downtown Reykjavik, in a former biscuit factory which has become one of the coolest venues in town.

The Burns celebrations form the opening night of Kex Hostel's inaugural Scottish Festival Week, a celebration of all things Caledonian with gigs every night featuring the likes of Withered Hand and Wounded Knee. Drummer Owen Williams provides the backbone of both, while also in attendance is artist Tessa Lynch.

Making up the rest of a band cheekily dubbed The Sassenachs are Icelandic bass player Pall Ivan Palsson and local hero Benedikt H Hermannsson. As Benni Hemm Hemm, Hermannsson has released several albums in Iceland and the UK, and spent two years living in Edinburgh.

Kex employee and Scots ex-pat Verity Flett, who moved to Reykjavik two years ago, had the idea for the Scottish Festival Week during a brainstorming session on how to liven up an otherwise quiet January. It was officially initiated at the behest of two of the venue's six shareholders: Petur Marteinsson – a footballer who once played for Stoke City – and film producer Kristinn Vilbergsson. The other four shareholders are also ex-footballers, who got involved in the project after Vilbergsson was sourcing locations, and stumbled on a then deserted building beside the sea.

Eighteen months on, Kex has enlivened a previously neglected part of Reykjavik, with cutting-edge artist-run gallery The Living Art Museum next door hosting an opening during Scottish Festival Week. During the second night's Kex show, Drew Wright (of Wounded Knee) and Williams improvise scratchy free jazz as Lynch reads the lyrics to Iceland, a song penned by Mark E Smith in 1981 when his band The Fall played in Reykjavik. The song is riddled with inaccuracies, say locals, but no-one seems to mind.

Marteinsson, Vilbergsson and Flett already have plans for a follow-up to Scottish Festival Week next year. They may be on to something. In the current political climate, with a Nordic-Scots alliance being mooted ever more favourably, there is infinite potential for further collaborations. Beyond Kex, there is also Airwaves, Reykjavik's premiere music festival, which, since 1999, has made the city even more of a musical hub than ever.

In 2011, Kex became a fringe venue for some of its smaller shows. With support on a par with that given to artists who attend the Austin, Texas-based South By South West festival, there is no reason why independent acts from Scotland couldn't be a force at Airwaves, with Kex as their base.

The final night of Kex's Scottish Week moves into a gym-turned-function room, in which a set of long wooden tables give the air of a mediaeval banqueting hall. Tonight's gig will be a more formal affair, with Wounded Knee supporting Icelandic singer Snorri Helgason, whose three-piece band play 57 varieties of quality Americana. Some kind of fashion show is on first, and Kex's bar is awash with what look like a party of Icelandic supermodels. With Wounded Knee and co going full pelt on Wright's own song, Pentland Jaunt, the table suddenly starts to shake. An artist from the exhibition opening next door is dancing precariously from end to end. With the band driving the music on, within seconds he's wheeched off the table in a fireman's lift by one of the be-kilted bar staff.

"Thank you for making me feel like I'm back in Scotland," Wright joshes, before introducing Freedom Come All Ye as a song that Nelson Mandela once suggested should be the anthem of the entire world and reinventing Hamish Henderson's inclusive internationalist hymn as a poundingly relentless avant-garde epic. At midnight on a Saturday night in Reykjavik in an old biscuit factory that's been transformed for the 21st century, it sounds like the future.

Neil Cooper stayed at Kex Hotel, Reykjavik,