Anticipating a rare visit by Jamie Cullum to Ronnie Scott’s this week, I joked that the shortage of headroom could curb the star’s enthusiasm for jumping on top of the piano. But not only did Cullum do that, he even had his members-only audience jumping up and down to the rampantly rocking Mixtape, at the climax of an engrossing set that featured a crack 12-piece band under the direction of saxist/arranger Tom Richards and was mostly devoted to Cullum’s imminent release, Interlude.

As often happens with Cullum’s jazz gigs, the cognoscenti can arrive expecting jazz-lite, and end up won over by this gifted and likable artist’s delight in the music and eagerness to share it. He arrived to deliver the album’s title track, with slinky brass riffs and former Sting pianist Jason Rebello’s delicate embroidery shadowing his smoky vocal. Cannonball Adderley’s soul-jazz classic Sack o’ Woe brought a bluesy tenor-sax break from Tom Challenger, and the abstract, ghostly The Seers’ Tower (“Sufjan Stevens filtered through Nina Simone,” as Cullum put it) began with a deceptive vocal tenderness and wound up in a storm. Nat King Cole’s Walkin’, then Lovesick Blues and Don’t Stop the Music followed fast, with Rebello and Cullum swapping the piano stool, and an increasingly relaxed and spontaneous Cullum eventually beatboxing and hand-drumming on the woodwork.

Declaring his 50s-era Sinatra influences (“when the singer is right in there with the band”), Cullum then showed just what he meant, as drifting woodwinds and trumpeter Fulvio Sigurtà’s fluent obbligato embraced him on a solemn Good Morning Heartache. Randy Newman’s Losing You drew Cullum’s most affecting vocal and also his most sensitive piano reflections, and an uninhibited You and Me Are Gone and When I Get Famous drove the show to captivatingly contrasting encores on Make Someone Happy (an elegaic duet with Rebello) and the rolling, rambunctious Mixtape.

• At Ronnie Scott’s tonight. Box office: 020-7439 0747. Interlude is out on 6 October.