Billed as a piece of 'gig theatre', Cover My Tracks is the vehicle chosen by former Noah and the Whale singer Charlie Fink to present his debut solo album of the same name. Aided only by an acoustic guitar and some backing track, Fink takes his seat on the Old Vic stage at 10pm - after Woyzeck - to play a collection of new tunes that you might loosely call a concept album. Its narrative gaps have been filled in with lines from the playwright David Greig, and Jade Anouka acts out the story arc that results from it all.

The low-key setup is directed by Max Webster, who so successfully teamed up with Fink and Greig for The Lorax at the Old Vic in 2015. Cover My Tracks offers a far gloomier spectacle than that Dr Seuss-inspired family fun, touching as it does on dark, depressive themes. Incorporating elements of folk tale and mystery, it concerns a young songwriter who suddenly disappears - is feared to have killed himself - and is then desperately looked for. This is by an ex-bandmate-and-lover, who uses clues in the musician's songbook to attempt to piece together his life and track him down.

The songs themselves – gentle, wistful things - include "I Was Born to Be a Cowboy", which is about thwarted ambition and the supposed death of rock and roll. Meanwhile, "Firecracker" reflects on the roles of luck and happenstance in life, especially the poignant life of a wandering musician. Always, the music in Cover My Tracks seems to have something meaningful to say about – well – music itself. It would be tempting to view the acting work as mere decoration between songs - but that would be to deny Anouka's captivating performance. She is vibrant and boundless next to the sedentary Fink.

To be fair, though, you don't normally associate theatrical qualities with solo folk music. In a way, the contradiction doesn't matter, because the story of Cover My Tracks is mainly interested in how you go about finding new artistic expression – and when to take risks. It's the dilemma that haunts the vanished songwriter character. "We have to now do everything except create a record," that tragic figure is supposed to have said, soon after he proclaimed the death of rock music. "In fact, we have to now make silence in the shape of an album!"

If less is more, then Fink and co have achieved a lot - rattling around the cavernous environment of the Old Vic late at night. The 'gig theatre' experiment will prove a novel way to sell records, no doubt. And the work is aware of its own contrivances – so much so that it feeds them back into its storyline. And even though it lacks the feverish unpredictability of the best gig, or the tonal range of the best theatre show, this is an ambitious genre-bending work that wants to say how damned difficult it is to make something original.

Cover My Tracks runs at the Old Vic until 17 June.

Watch Charlie Fink and Jade Anouka in rehearsals for Cover My Tracks