Bob Dorough and Friends, Pizza Express Jazz Club

Aged 91, and as frisky as a newborn puppy, the US singer, pianist and songwriter Bob Dorough is a sui generis stylist whose smart lyrics – delivered in an understated southern brogue – and nimble pianism which nods to both bebop and swing masters, combine to produce something quite unlike anything else in jazz. But what really lit up the Pizza Express Jazz Club was the joie de vivre of Dorough's performance, his humour and love of the ludic.

The gig saw him reunited with the London-based musicians who facilitated and played on his terrific 2006 album for the Candid label, Small Day Tomorrow: the dynamic rhythm section of bassist Geoff Gascoyne and drummer Sebastiaan de Krom, plus vocalist Trudy Kerr. Sarah Moule, another great vocalist who knows and loves Dorough's work, completed the core quintet ("they're my Bobettes," said Dorough).

Covered by Diana Krall, Claire Martin, Jamie Cullum and others, it was a delight to hear Dorough sing it in the flesh

The beautifully paced first set ranged from Dorough's newest song, the rather lovely “Summer Solstice”, whose metric shifts typify the trenchant individuality of his writing, to his best known, the brilliant "Devil May Care". Providing the title of his 1956 debut album, and covered by Diana Krall, Claire Martin, Jamie Cullum and a host of others, it was a pure delight to hear Dorough sing it in the flesh, switching from playful to lyrical with absolute ease. We also heard the first of many apposite solos from Gascoyne.

Other first set standouts included "Nothing Like You", the first song that Dorough co-wrote with Fran Landesman, which he sang, famously, on Miles Davis's 1967 album Sorcerer (the song was recorded at an earlier session). Esperanza Spalding, no less, has declared it one of her favourite songs. Dorough's vigorous piano chords came flying out of the traps but, in all the excitement, his vocal stalled. "I forgot to sing," he exclaimed, before circling around the tune again. Given that these were mostly new arrangements, a little leeway was surely allowed.

The poignant "Scars", another terrific Landesman lyric with music by Simon Wallace, was performed – perhaps for the first time – as a three-hander, with Moule and Kerr contributing their rich, mellifluous tones to an, at times, almost jaunty take on what is usually an anguished ballad ("Don’t be ashamed, everybody’s got scars, from our various wars, on the way to the stars"). Its composer was standing a couple of feet away from me – I can't be sure, but I think he liked it. Spreading the love a little, we also got to hear Gascoyne's "Keep It To Yourself", with Dorough interjecting little whoops between phrases, and Derek Nash – another member of Dorough's London team – contributing a potent tenor solo. Then, to conclude the set, what else but the king of slacker anthems itself, "Small Day Tomorrow", another Landesman and Dorough confection.

With the quintet really beginning to relax into the music, an even more impressive second set was stuffed with great things. Featuring words by Dave Frishberg and music by Dorough, a song they recorded on their Blue Note duet album Who's On First? (2000) and covered by everyone from Blossom Dearie to Bette Midler, “I'm Hip” was a bona fide, laugh-out-loud classic (“Now I'm deep into Zen, meditation, and macrobiotics, and as soon as I can, I intend to get into narcotics”), performed with real zip and wit here. Dorough also clearly had a ball with the ennui of Frishberg's “Another Song About Paris”.

It was impossible not to be carried away by the warmth of the music-making

A joyous duet with Kerr on Dorough's tricky original “Up Jumped a Bird” recalled the fine version by the same pairing on Kerr's 2007 album Déjà Vu. Whether it was the soulful "Comin' Home Baby", a hit for Mel Tormé in the 1960s, or the wonderfully titled, quietly touching “Love Came On Stealthy Fingers”, song after song had you marvelling at Dorough's 24-carat compositional gift.

For the final number, we were treated to an adrenalised romp through “I've Got Just About Everything”, with a towering scat from guest vocalist Anita Wardell over a deep groove from Gascoyne and de Krom. It was impossible not to be carried away by the warmth of the music-making. Still gigging, still recording – released last year, his most recent album Eulalia is well worth investigating – Bob Dorough shows no sign of slowing down. And for that we should rejoice.

• Visit Bob Dorough's website