The art world can't get enough of Ragnar Kjartansson. Hot on the heels of two Venice Biennale offerings for Iceland and a host of new commissions across America, the 40-year-old contemporary performance artist is at the top of his game. It's quite incredible, then, that this summer's eponymous Barbican exhibition is Kjartansson's first solo show in the UK.

'If we hadn't done it now, someone else would have,' explains the exhibition's associate curator Leila Hasham. 'The problem is, staging something so varied and performance-based is expensive and difficult.' Galleries without the luxury of space and finance have shied away from such an extensive survey – until now. The Barbican, with its theatrical, cinematic and artistic expertise, is the ideal home for Kjartansson's varied ouevre of films, paintings and live performance.

Kjartansson thought so too. 'The interdisciplinary buffet that is the Barbican fits my unfocused practice. Seriously, I love the building, the utopian feel and the programme that has kept me coming and coming as a tourist since my parents took me here in the 1980s.'

Kjartansson grew up backstage at Reykjavik City Theatre, and his theatrical parentage shines throughout the exhibition – his actress mother even features in one of the earliest works, Me and My Mother (2000). The film depicts her spitting in his face repeatedly, in a provocative, yet laugh-out-loud take on a loving, motherly relationship.

But the work that's got more tongues wagging than any other is Second Movement (2016), a four-hour-long kiss staged on the Barbican lake every Saturday and Sunday for the duration of the exhibition. Kjartansson wanted to create something similar to his 2013 Venice Biennale performance SS Hangover, wherein a large fishing boat from 1934 swayed with a host of brass musicians. 'I told him that was all well and good, but our pond was only 50–60cm deep,' Hasham explains. He went away and thought about it, returning with a bespoke, hand-painted rowing-boat with a flat bottom that could skim the shallow pool with ease.

The resulting performance, in which two women in Edwardian dress are frozen in an elegant embrace, appears at once peaceful and obsessive, innocent yet voyeuristic. The overriding impression is how small the two girls look, performing with calm confidence while the brutalist architecture looms absurdly above them. One might assume that only jobbing actors could keep such an intimate hold with professionalism; but they were sourced through the 'Barbican Creatives' Facebook group, advertised on social media and through the trade union Equity.

Hasham asked Kjartansson why he chose to work with two women. 'He said it was down to his interest in repetition, reflection, mirror-images,' she reveals. The two girls reflect each other's gentle movements completely, which are then mirrored in the dark water below. Second Movement is site-specific to the Barbican, and cannot be recreated elsewhere. Catch the perfect embrace before it disappears forever on 4 September.

TAGS: BARBICAN CENTRE, PERFORMANCE ART, ON INSTAGRAM