"After that, who knows what'll happen. Maybe we'll stage an impromptu performance of The Lion King," says Jeff Tweedy, running us through what he may or may not have up his sleeve for the final third of tonight's show. He pauses. "This is an impromptu performance of The Lion King. All music is."

He's joking, of course (though at one point does look to be mulling over a burst of 'The Circle Of Life'), but the nod to his surroundings, the London Palladium, is actually quite fitting: tonight finds Tweedy performing his own personal variety show, moving backwards through material from his first solo album, this year's Sukierae, recorded with his son Spencer (and discussed in our interview) who joins him along with a three-piece band, to a solo acoustic set of Wilco and Uncle Tupelo songs and closing with some golden choices from the Mavis Staples records he produced.

They open up with 'Nobody Dies Anymore', one of Sukierae's most plaintive moments and disarming as a choice of first song, meditating on the unceasing sadness that would come if science began endowing us with eternal life. In a live setting, with some of the rough-edged production tweaks on the album absent, it's the tone of Tweedy's voice that comes through most, the image of people "sober/ To a depth we don't own" freighted with a very real poignancy. As reedy and quietly expressive as it is on record, here it's shaded with a brittleness that's of a piece with the songs; not the breathless howl of 'Kicking Television', but one possibly frayed - Sukierae is named in honour of his wife, who has been battling a cancer now in remission - by a year of personal strife. Elsewhere, it scales upper registers with a clarion prettiness, as on 'Summer Noon', underpinned by gently ringing guitars, or the cover of 'Love Like A Wire' by the late Chicago singer-songwriter Diane Izzo. Tweedy's assembled a band capable of tapping some of Wilco's most formidable traits, guitarists Jim Elkington and Liam Cunningham working up rapid frisks of febrile noise on 'High As Hello' or the skewed, wavering slide guitar drone that underpins 'Fake Fur Coat'. This, though, segues into 'Diamond Light, Pt. 1', which the band make entirely their own: Spencer Tweedy and bassist Darin Gray hold down a tight rhythmic interlock over which the guitarists play out an expansive instrumental middle passage of jagged fretboard mangle.

With the rest of the band gone, Tweedy moves into his solo turn, 'I Am Trying To Break Your Heart's familiar cycle of chords welcomed with an appreciative roar from the audience, now sunk into an intimate darkness. Shorn of the jumble of sonic fragments strewn across the Yankee Hotel Foxtrot version, it's even more direct, verses tracing inebriated remorse linked by wiry guitar breaks, resplendent in the theatre's pin drop-silence. The mixture of songs he follows with is an impressive testament to over a quarter-century's worth of recorded output: there are further Wilco favourites - a louche, jazzy version of 'Hummingbird', 'Jesus, Etc.' and 'I'm The Man Who Loves You' - lining up alongside a couple of cherry-picks from recent albums, Wilco (The Album)'s 'One Wing' and 'Born Alone' from their last full-length, The Whole Love, as well as 'Passenger Side' from the other end of their catalogue, 1995's debut AM. 'New Madrid' sounds even better solo than it did on Uncle Tupelo's swansong Anodyne, occupying lyrical and musical territory that feel decades older than its 1993 vintage, as do two fine choices from Tweedy's non-Wilco work, Loose Fur's 'The Ruling Class' and Golden Smog's 'Please Tell My Brother'. The wry between-song chatter, familiar to anyone who's seen the Sunken Treasure film, emerges, Tweedy delivering some dryly hysterical rejoinders to calls from the audience in his Midwestern burr. Someone in the stalls shouts their intention to take him home for a guitar lesson. "Is that what they're calling it nowadays?" he asks, before pausing and adding: "You would not want a guitar lesson from me... It would probably be worse than having sex with me."

He waves goodbye after 'A Shot In The Arm', but returns, band in tow, for an encore of Mavis Staples' 'Only The Lord Knows' and 'You Are Not Alone', followed - "we're going to play a couple of songs that share all of the same chords - because of the economy" - by Uncle Tupelo's version of Sir Doug & The Texas Tornados' 'Give Back The Key To My Heart' and 'California Stars', perhaps the best of Wilco and Billy Bragg's settings of Woody Guthrie's songs. It's an amped-up version that sees Elkington and Cunningham trading solos, allowing Tweedy to take a backseat and observe. While it's a very funny gig, the humour curiously throws certain aspects of his songs into sharper relief. It may be that, in light of the year's events, 'Sunken Treasure's sentiment "music is my saviour" - even if not aired tonight - rings truer than ever for Tweedy. As much as his catalogue is, as he sings on 'Honey Combed', figuratively "written with a rope/ Wrapped around my throat", its uniting theme is redemption. There's something wonderful in seeing an artist unfurling such a set of songs over these two hours, pared back to their barest, in some ways most luminous form and rendered with an unshowy brilliance.

Tweedy play four more dates on their European tour this month, before returning next year, playing Vicar Street in Dublin on January 28 2015, Glasgow Royal Concert Hall, 29, and The Ritz in Manchester, 30; head to their website for full details and tickets