Another sold-out gig, another standing ovation, another memorable night. A sprightly 89 years old, the vocal pipes may not be quite so silky, but on the first of a three-night run at Ronnie Scott's, Jon Hendricks – dubbed the “James Joyce of jive” by Time magazine - still had the chops to show why he's considered one of the most original and influential singers in jazz.

When Mavis Staples opens her mouth, remarkable things happen. She hollers, she sobs, she moans, she swoops, she rasps, she croons, she shudders. Not since I last saw Al Green have I seen such a bravura display of vocal prowess. On a rainy night in London, the 71-year-old singer of gospel, soul and R&B was in town for a one-off gig (and also for a Jools Holland appearance) to promote her new album, You Are Not Alone.

For me there is a trinity of black musicians, visionaries who reshaped music in the last half-century: James Brown, Miles Davis and Fela Kuti. And just as it’s hard to imagine a biographical musical of James Brown or Miles Davis coming off - because which mere actor is ever going to have their charisma, attitude or moves - likewise it seemed a stretch to imagine Fela! being much more than sophisticated karaoke. Karaoke with a message and some groovy dancing, no doubt. But somehow this production pulled off the impossible. Near as dammit anyway.

A member of Miles Davis's legendary second quintet (“arguably Miles's best ever group” according to the Penguin Jazz Guide); a composer of standards (“Watermelon Man”, “Dolphin Dance”, “Maiden Voyage”, “Cantaloupe Island”) and soundtracks (Antonioni's Blow-Up, Bertrand Tavernier's Round Midnight); winner of over 10 Grammy Awards, the first for his 1983 hit single “Rockit”, the most recent for his magnificent 2007 Joni Mitchell tribute album River: The Joni Letters (one of only two jazz recordings to win the coveted Album of the Year award, the other being Getz/Gilberto over 40 years ago). Whichever way you cut it, pianist Herbie Hancock is one of the lodestars of American music, whose influence reaches out far beyond the narrow confines of jazz. A brilliant extended set from this bona fide jazz icon brought a capacity RFH audience to its feet.

There were times during this show when there was so much happening, I didn’t know where to look: at Damon Albarn, driven by musical demons, roaming the stage, singing his heart out, or just grinning, his gold tooth glinting? At the two former members of The Clash who are currently part of the Gorillaz line-up, Mick Jones and Paul Simonon, the latter in particular the absolute epitome of cool in his sailor’s cap and his leather jacket with the collar turned up and his low-slung bass? At the Hypnotic Brass Ensemble, the Chicago band whose swaying horns were such a vital part of the evening? At the silhouetted string section, also in sailors’ caps, lined up across the back of the stage? At Bobby Womack, soul legend and man of infinite dignity, singing “Stylo” (from this year’s Plastic Beach album)?

There were times during this show when there was so much happening, I didn’t know where to look: at Damon Albarn, driven by musical demons, roaming the stage, singing his heart out, or just grinning, his gold tooth glinting? At the two former members of The Clash who are currently part of the Gorillaz line-up, Mick Jones and Paul Simonon, the latter in particular the absolute epitome of cool in his sailor’s cap and his leather jacket with the collar turned up and his low-slung bass? At the Hypnotic Brass Ensemble, the Chicago band whose swaying horns were such a vital part of the evening? At the silhouetted string section, also in sailors’ caps, lined up across the back of the stage? At Bobby Womack, soul legend and man of infinite dignity, singing “Stylo” (from this year’s Plastic Beach album)?

Brad Mehldau is a cool cat. An intellectual one, introverted to the point of semi-autism, precise and clear. A strong mystique based on critic-proof good taste and hardly talking to anyone, least of all many music journalists (I’ve tried). At least that’s what I used to think before last night’s extraordinary show. He still looks a bit of a nerd, hunched over his piano and pale as a baby polar bear locked in the attic for too long, but this was a warm, enveloping trip of a gig. The 21st century is the century the nerds took over - Gates, Zuckerberg, Mehldau. The jocks, the lookers, the sexy ones: your time is up - you really should have been concentrating in algebra, after all.

And we're off. Marking the official start of the London Jazz Festival, “Jazz Voice: Celebrating a Century of Song” provided a superbly paced and brilliantly conceived curtain-raiser. Hosted by Scottish actor Dougray Scott and presenting vocalists from both sides of the Atlantic, this paean to the art of song featured Guy Barker's consummate, high-spec arrangements lovingly performed by his hand-picked orchestra.

There’s a moment during Hjaltalín’s encore when bolero rhythms take over and you wonder if the Reykjavik septet have invented a new musical hybrid: a Ravel-driven makeover of Seventies-slanted soul. As singer Sigrídur Thorlacius lets rip on the thrillingly anthemic “Feels Like Sugar”, it’s clear that Hjaltalín aren’t bothered with current musical templates. They take from the unlikeliest sources, smoosh them together and end up sounding like no one else. After all, this is a band with a stand-up bassoon player.