Some time in 1979 I was at a gig at the Electric Ballroom when a sharp-dressed man with a prematurely balding dome and pallid complexion walked past me. He was not a looker by any means, but he had a stunning girl on his arm. I recognised him as Joe Jackson; and his debut single came instantly and inevitably to mind.

The title – Is She Really Going Out With Him? – surely resonates with every man who has felt a sense of inadequacy seeing “pretty women out walking with gorillas” in the street. Jackson’s blend of humour and pathos captured it perfectly.

When he arrived on the New Wave scene it was tempting to dismiss him initially as a ‘new Elvis Costello’ with his penchant for sharp suits and strangled vocals, reggae rhythms and punchy guitars.

But with his first three superb singles, all taken from debut album Look Sharp – the reggaeish Sunday Papers, the punkish One More Time, and this one – Jackson quickly staked his own claim to musical fame.

Criminally and bafflingly, none of them charted at the time (though this one would reach No.13 after re-release a year later).

Since then, the classically trained Jackson, who had studied composition, orchestration, percussion and piano at the Royal Academy of Music, has enjoyed a career that has run pretty parallel to Costello’s without ever achieving the same level of mainstream fame.

Like Costello – and his own idol George Gershwin – Jackson’s impressively vast musical output straddles many musical genres, marking him out as a restless and multi-talented polymath.

Surfing in initially on the New Wave, he edged further towards reggae before becoming a jump blues revivalist, a salsa singer, a jazz crooner and then, in a 180-degree turn, a Grammy-winning composer of classical music and film scores, returning to jazz for a Duke Ellington tribute album that included a duet – It Don’t Mean A Thing (If It Ain’t Got That Swing) – with Iggy Pop.

Among his more ambitious projects are his 1999 Symphony No. 1, played not by an orchestra, but by a band of jazz and rock musicians including virtuoso guitarist Steve Vai, which won the 2000 Grammy Award for Best Pop Instrumental Album.

His memoir, A Cure for Gravity: A Musical Pilgrimage, recounted his life and career, with the happy conclusion that: “I’m still making music, no longer a pop star – if I ever really was – but just a composer, which is what I wanted to be in the first place.”

Not bad for a working-class boy who grew up with asthma in poverty in Portsmouth.