Elvis Costello & The Brodsky Quartet, Barbican, London

Elvis Costello begins with “Accidents Will Happen”, sung as he sang it in 1979 when he was a New Wave pop star, but played by the classical strings of the Brodsky Quartet.

Cheers for this old favourite are checked in the hush of a classical space. Such confusion has followed Costello for most of the 15 years since his album with the Quartet, The Juliet Letters, announced his interests had outgrown even the restless pop pastiches of his earlier work.

On record, this has rarely resulted in work as relentlessly brilliant as his peak years with the best rock’n’roll band of their time, the Attractions. There have been many moments since when chutzpah has become hubris, as when he re-arranged “Watching the Detectives”, replacing the right notes with wrong ones, on his equally quixotic chat show Spectacle.

But during tonight’s two-and-a-half hour show every musical barrier melts, and my heart with it at times. Costello looks like a dapper, moustachioed crooner in a 1950s LA dive, or a menacing minor hood. He more or less stands still at first, maintaining the pretence of a classical recital but pawing the ground. Holding his hand out imploringly, he could be one of the Supremes. Finally he spins away from themic, to stalk the stage with precisely dramatic effect.

His voice, which, like his lyrics, had become a strangled parody recently, is blessedly unclenched, as it is on his fine upcoming LP, Secret, Profane and Sugarcane. Supple and daring singing lets him sink into the character of a lonely man who’s a ghost in his own life in “Either Side of the Same Town”, then leap into a falsetto Southern soul cry.

On the Patrick Kavanagh poem “On Raglan Road”, the Quartet’s Jacqueline Thomas whacks her cello with her bow with jazz insolence, till this Irish reel settles into a serene meditation. “I Thought I’d Write to Juliet”, a song of the first Gulf War, gives the Quartet a long, sad section of their own, letting the mournful theme hang in the air for inspection. It’s as this slips into hard blues picking on “Bedlam” that I realise the brakes are off, and this is a Costello show, classical or not.

The perfectly pitched longing of Johnny Mercer’s “P.S. I Love You” is a forgotten masterclass from the American songbook, which the emotional simplicity Costello is discovering in ballads such as “Still” aspires to match. Such delicacy and melodic craft is worth his periodic abandonment of rock bile.

The other heartbeat of this show begins with “All This Useless Beauty”. “Nonsense prevails/ modesty fails,” he sings sadly, of any year you care to name. “Leaders still feast/ on the backsides of beasts,” he continues with deadly contempt, at theirs for us. The gentleness of approach puts the betrayal – sexual, social – which is his subject in starker relief. “Pills & Soap”, his 1983 broadside at Thatcherite and media excess, sounds more horrible because not one word needs changing.

Every line of “Shipbuilding” then unlocks bottomless emotion. “Diving for dear life/ When we could be diving for pearls,” Costello quietly pleads in the most perfectly poetic anti-war song, as if finally trying to be heard. The spaces left for the Quartet hold up the tear-jerking rush, as they sometimes do elsewhere, in a slightly over-complex arrangement. All five musicians are reaching for new feelings, and here they try just too hard.

But then there are folk songs, and faux hymns, and the new album’s riotous Americana travelogue “Sulphur to Sugarcane”, which needs dancing it won’t get tonight. “The Birds Will Still Be Singing” gives hope, and the Quartet, the last word, as nature eases and outlasts the bleakest times, and strings weighted by Thomas’s deep, dark cello uneasily contemplate the fact. Music is a wide open frontier to Costello, and we’ve glimpsed its horizons.

Touring to 29 April