First thing I wanna say: Alabama Shakes are in good hands. The producer of their second album, due soon, is on stage at Bush Hall tonight and is, second song in, playing Joe Tex’s “I’ll Never Do You Wrong” up a storm, his unfettered guitar slashing out a solo that is terrifyingly “backwoodsy”. He isn’t going to lose the Shakes spontaneity, that’s for sure. His Coodercaster-style guitar has a pickup that sounds like a swarm of bees, apposite considering Joe’s wonderful lyrics for that song (“And if I ever make you cry/Baby, I hope a fly alight on my pie/I hope a bee sting me over my eye”), but his syncopated style puts me most in mind of Lowell George, another great songwriter/guitarist with an unusually broad musical worldview. Seated for the whole gig, Mills would often take delight in a particular phrase and caress it again and again, smiling to himself all the while, especially when leading the band to the brink of a canyon of noise, to only let it all fall away, opening up a cavernous gap filled only by the sound of reverb throbbing its way into the distance…

At various points you could say Manuel Galban or Les Paul, or, I don’t know, Dick Dale, Chet Atkins, Eddie Lang and Lonnie Johnson. I’m not trying to pigeonhole, just trying to get a little of the flavour of someone who – combining great taste with an experimentalist’s bravado – takes the audience (which tonight includes Don Was and Marcus Mumford) on a sonic tour of all the places a guitar can go. Some songs sound beamed in from the mazy dreamscape of an American midnight, where you hear the gaps between the radio stations and the signal comes and goes. Others (the “Who Do You Love” riff, bludgeoned – thrillingly – for about six minutes) show that taking the volume control down to one doesn’t negate his love of turning it up to 11. Oh, and I’ve never seen a performer hit his guitar as much as Mills, either thumping the upper bout or wrenching the body back from the neck for a little improvised tremolo.

With a fine rhythm section of Stuart Johnson, on a kit that includes an enormous Marching Bass Drum and – I think – no hi-hat, and Sebastian Steinberg on deep, deep bass, with Tyler Chester on vintage keys (Chamberlin, Mellotron and Wurlitzer) the music could flip between a swampy ZZ Top boogie and a wistful Randy Newman vibe with ease. The switches in tone  were jagged and dramatic, but they always made sense. Fiona Apple joined in for a suitably gothic/gospel version of Conway Twitty and Jack Nance’s “It’s Only Make Believe” and a couple of the songs that she sings on Mills’ new album, Heigh Ho. After an audience meltdown brought them back for an encore, we were treated to an extraordinary cover of Lonnie Johnson’s “Tomorrow Night” that was part-Elvis, part-Twin Peaks (it owed a lot to Chester’s fifties sci-fi soundtrack organ). In a burnished croon, head flung back and eyes closed, Blake Mills sang it to the rafters, and then soloed with a hushed, dampened series of semi-atonal Les Paul phrases. I realised that for most of the gig I had been leaning forward, not to watch his fingers, but because the music somehow demanded it.

The are some good videos online, but nothing really replaces sitting twenty yards from his amplifiers. Fretboard Journal has a fascinating hour-long interview here.