Gurrumul, Barbican, London

Before Aboriginal culture's greatest ambassador takes the stage, we hear a series of vox pops from those he represents.

One says Geoffrey Gurrumul Yunupingu is "making a bridge, telling our stories; it's very important to us". No pressure, then, as he deftly combines his traditions with western instrumentation.

Thankfully, Gurrumul is adept at deflating world music earnestness, something that goes beyond ditching the didgeridoos. It is easy to be precious about the blind musician from northeast Arnhem Land, but an easygoing humour runs through tonight's set that makes this theatre feel more intimate.

Partly this is due to the easy rapport between Gurrumul and close friend Michael Hohnen – producer, double bassist and interlocutor for a generally taciturn performer. This evening is no exception, until Hohnen alludes to how, like Bob Dylan, the singer/guitarist does not talk to his own band. Sure enough, during the next song, a gruff voice shouts, "Yo! Take it away boys." With smart comic timing, Gurrumul breaks his silence.

Such repartee helps break the trance-like spell of the artist's wondrous tenor voice and a reminder he is already a veteran performer. During the Nineties, Gurrumul toured the world with fusion rockers Yothu Yindi, before returning to his homeland to join the reggae-influenced Saltwater Band. Yet it was the minimal accompaniment on his 2008 eponymous solo debut album that allowed us to properly appreciate the most distinctive vocalist to emerge from Oz in the past couple of decades.

A more contemplative follow-up record, Rrakala, polishes Gurrumul's sound without overpowering the vocals, a strategy that continues on his only UK date of a short European tour, his first since 2009 and recovery from a debilitating illness. In a varied set, he largely plays with a four-piece band, Hohnen plus extra guitar, piano and drums. Singing in various first-nation tongues, Gurrumul easily fills the cavernous space with a soft, soulful delivery that floats over supple, flowing melodies.

On previous dates, translations of his lyrics were projected on stage, but this is not Italian operetta. Whether, according to Hohnen's explanations, Gurrumul is singing about crocodiles or fish, the real subject matter is his visceral need to connect to nature and the place he is from. Simply with his ally's backing, this music is powerfully charged, while the band add drive to more celebratory numbers. "Mala Rrakala" has a spicy Hispanic rhythm, a feeling attenuated by how Gurrumul's strums and rolls his "r's".