Loudon Wainwright III and Richard Thompson, Royal Festival Hall, London

The programme for Richard Thompson's Meltdown festival carries a photograph of Thompson in his salad days – taken, probably, in the late Sixties or early Seventies, some time around his founding of Fairport Convention and his marital and musical union with Linda Thompson. A little Nick Drake-like, he gazes wistfully off-shot. It feels iconic. But while for a lot of people Thompson's name might ring a bell, ask them to hum one of his tunes and you'll probably draw a blank.

Unquestionably, the man and his music should be much better known. The same might be said for Loudon Wainwright III, the other half of a double-header tonight, if it wasn't for the fact that his children, Rufus and Martha, have been doing their best to buff up the family name. He's down as folk but listen to those blues scales and watch the way he twists and jerks over his guitar, pouring his caustic observations and misanthropic itches and his very soul into a bundle of fine songs. His playful take on the afterlife, "Heaven", is rapturously received and numbers from his latest album, 10 Songs for the New Depression, are vintage: bathetic, rueful, funny.

Thompson is a revelation and his relative obscurity in comparison to previous Meltdown curators (Costello, Bowie, Morrissey) is swept aside in a blaze of bravura musicianship. He and Wainwright each take to the stage with only their guitars, but such is the colour that Thompson wrings from his instrument that he may as well have a harpist or a mandolin player or a whole choir standing behind him.

On "Sunset Song" he raps his bottom E while picking out a flighty, gorgeous melody higher up the strings; "Beeswing" and "1952 Vincent Black Lightning" are elegant highlights, love songs in the folk tradition. Thompson's rich timbre, a folkish thrum with a hint of Dylan, is of such quality that it shouldn't need any description at all.