Naming your band after your musical hero – in this case the legendary American old-time singer Ola Belle Reed – is dangerous; but this five-piece New York ensemble have no need to worry about doing their namesake justice. Richard Thompson describes Ollabelle's sound as the sole successor to the Band's 1968 album Music from Big Pink; and while you can tick off their influences as they play – gospel, bluegrass, Appalachian, blues – you still reach the end of the evening with the sense that you've never heard anything like them before.

They start the evening, naturally, with one of Reed's songs, but soon segue into an unexpectedly dark place. A bluesy John the Revelator has a suitably apocalyptic sound – this is blues for the end of time – and the gospel song that follows is almost as black. Fiona McDay sings with hypnotic, seductive power about old-testament Elijah while guitarist Jimi Zhivago – who, next to McDay's elegant silhouette, looks like a roadie who's accidentally stumbled onto the stage – rolls out devilish riffs.

To say the set lightens up as it progresses would be an overstatement – even the most upbeat country moments retain a hint of mourning, and McDay jokes at one point that all the best songs are about death – but they shift effortlessly through the musical gears. Lullabies and ballads are punctuated by a jazz number with a spectacular piano solo, and when bassist Byron Isaacs takes over the vocals they even prove they can get a little nasty. Then, as if their versatility needs any further proof, they switch instruments and the drummer takes over the lead for a song by Taj Mahal.

If a four-part harmony version of the Rolling Stones' I Am Waiting hits a comparatively weak note, it's only because the rest – especially their own oeuvre – has such depth. Their sound pools like an unfathomable body of water in a cool, dark cave. And while their versions of Down By the Riverside and Jesus on the Mainline are bona fide spine-tinglers, the most effective of all is a spiritual of their own, Heaven's Pearls – a soothing balm to troubled hearts and times.

Olabelle performed at the Meltdown festival on 16 June. Richard Thompson's Meltdown continues until 21 June.