Alejandro Escovedo, Bush Hall, London

Alejandro Escovedo is more cult figure than household name, but over the last few years he's started getting some of the kudos he deserves – and just in time, given that he almost died in 2003 of Hepatitis C. Friends and musicians, including Steve Earle and John Cale, released a tribute album to help pay his medical bills, and after the strings-drenched The Boxing Mirror in 2006, his latest album, Real Animal, is an intense musical memoir that ranges from his youth in California to the punk years in New York and later in Austin.

He's a musician who cuts his cloth close to the bone, even in his fifties looking the archetypal black-suited, first-generation American punk – which indeed he is, or was. His first band, The Nuns, opened at the Sex Pistol's last-ever gig in San Francisco; his next, Rank and File, pioneered alt-country.

Escovedo, accompanied by David Pulkingham on guitar, is an engaging, immediate performer from the off, taking possession of a packed audience at the Bush Hall by walking down into the aisle to perform, sans amplification, the wonderful "Five Hearts Breaking". They follow it up – on the stage – with the amplified acoustic riff of "Always a Friend", the song Escovedo recently performed with Springsteen and the E Street Band in front of 75,000 bikers in America. Tonight's audience is less hirsute, but Pulkingham still strikes his strings as if they were mortal bonds, delivering an urgent take on the song.

The songs of Real Animal, which dominate the set tonight, flex a lot of narrative as well as musical muscle. Some look back at the wild side of life – Sid and Nancy in "Chelsea Hotel '78" – while others address earlier, more idyllic concerns, such as the ballad "Swallows of San Juan" that evokes memories of early Sixties California.

The new songs' acoustic settings often supersede their shiny studio versions, and sit well beside the handful of career classics – the Mott-the-Hoople influenced "Castanets", for example, that somehow made it on to George W Bush's ipod (Escovedo stopped performing it for three years when he heard). After several standing ovations, Escovedo closes with an emotive encore of the Clash's "Stand By Me".

"What a beautiful place to play an acoustic guitar," he says, looking around him at the hall's unique interior. With nights like this, Escovedo is never going to be short of good friends.