It's an extraordinary thing to see a slight figure alone on stage at the Old Vic, a 1,000 seat theatre most recently home to the massed ranks of Groundhog Day and soon to be hosting the massed ranks of King Lear. So I applaud the courage of the actress Lisa Dwan (and the artistic director Matthew Warchus) for simply being there, and filling the vast space with this haunting interpretation of Samuel Beckett.

No's Knife is not a play. It is based on Texts for Nothing, a collection of prose pieces that Beckett himself described as "an afterbirth" to his three great novels. Dwan, who has adapted the work for theatre with the encouragement of the Beckett estate, sees it as a bridge between early Beckett and the haunting final plays.

It was with a trilogy of those – Not I, Rockaby, Footfalls – that she made her name as a Beckett interpreter, and this full-blooded, heart-felt performance will only enhance that reputation. She is astonishing, conjuring a multitude of voices, and finding a way of making these difficult words live and compel as part of a stage performance.

The evening, co-directed by Dwan and Joe Murphy, opens with her closed eye, billowing on a silk screen at the front of the stage. Then we hear her breath, and as the eye opens the focus pulls in until we are left only with the pupil, a circle of blackness. Images of her swimming down to the deep give way finally to the live vision of her pinioned – in Christopher Oram's design – in a cleft in the rocks, or a crack in the boggy peat, "down in the hole the centuries have dug."

She seems to be standing and lying, trapped and cosy, a visual representation of the state between nothingness and something that the words return to over and over again. Later, in four separate sections, we see her standing in a barren landscape of stone, and suspended above the stage in a cage, her own judge and party, witness and advocate, noting her own state of being, answering her own disembodied voice – the voice of reason, which duly notes her testimony.

Finally, in a moment of surprising intimacy, she comes right to the front of the Old Vic's thrust stage, the huge grandeur of the proscenium arch behind her, and captured in Hugh Vanstone's soft light, grapples with the questions of being and not being, of a soul lost but in communion with the dead and the living, of a voice trying to be heard.

It is often moving, full of Beckett's poetry, rolling in arresting phrases – "malty night", "besotted in brotherliness" "swaying like a ladder of smoke". Occasionally, it is illuminated by flashes of humour. It is always compelling, but the text is dense and elliptical, giving voice to a lost soul, battling nothingness, surrounded by the din of other phantoms, other ghosts. But it doesn't, for all Dwan's animating efforts, feel quite theatrical until the final section when her cry "Where would I go if I could go? Who would I be if I could be?" suddenly shoots from the stage straight into the heart.

No's Knife runs at the Old Vic until 15 October.