This beautifully brooding slice of English pastoral places Cecil Sharp, the godfather of folk music who collected thousands of songs from rural communities, alongside two women he met in 1903. They were half-sisters, Louie Hooper and Lucy White, daughters of a renowned singer in south Somerset who, at the start of this drama, has just died, leaving them drenched in grief.

It is clear why Nell Leyshon’s script was adapted into a BBC audio drama last year, starring Simon Russell Beale and Amanda Wilkin. It bursts with sound, from distant birdsong to folk tunes the sisters sing as they sew gloves to make ends meet.

But the visual aspects of this production are just as enthralling with Matt Haskins’s dappled light throwing shadows across Rose Revitt’s simple, striking set, sometimes lighting up the sisters with the clarity of a Vermeer painting to capture the everyday drama of bucolic working life.

Sharp’s meeting with Louie and his appropriation of her songs lie at the play’s heart, though the sisters’ relationship runs deftly alongside it. The production is paced to perfection by Roxana Silbert and full of delicate but deeply mined emotions, every actor shining in their part.

Song is finely integrated into the script with spine-tingling moments when Louie (Mariam Haque, quiveringly expressive) sings her haunting solos. Lucy (Sasha Frost, just as brilliant as the more flirtatious, frustrated sister) intermittently joins in along with her sometimes lover, John (Ben Allen), to give the play a bustling community feel.

Simon Robson’s Sharp is a slyly manipulative figure, quickly switching on the charm when he sees his opportunity with Louie. He goes from cajoling her into singing her mother’s songs for him, even when her grief is raw, to the full-circle betrayal of handing over a book of those songs now “tidied up” and appearing under his authorship.

Like Jean Rhys’s 1962 short story, Let Them Call It Jazz, about a Caribbean woman whose song is taken and sung by a man at a west London party, Leyshon explores questions around the archiving and ownership of an oral tradition, capturing all the nuance in the debate, from whether it needs preserving in this formal way to if it can remain authentic in that process.

Sharp, who has since been accused of racism and misogyny, not only flattens out Louie’s songs but projects his jingoism on to them. “I see England,” he says when he first hears her sing and speaks of the “purity” of Englishness in her sound, seeing her as a “primitive” force within the land, which sounds close to Rousseau’s Noble Savage.

For her, songs are also connected to the land but without his toxic nationalism; as she points out, the songs were passed down to her mother by her “Gypsy” father, who collected his verses through his travels. Where Sharp wants to fix Englishness on to the page in his compositions, she tells him, wisely, that “none of it stays still” and this aspect of the play speaks to contemporary anxieties over nationhood and identity.

The play’s intellectual explorations never overshadow its emotional drama; we feel Louie’s betrayal and also a strong sense of the sisters’ complicated bond. Louie’s dependency and Lucy’s desire to leave creates a tension resembling Tennessee Williams siblings. The tenderness between them develops slowly and powerfully, the story in the end as much about their songs, indelibly tied to love, grief, memory and Somerset itself, as it is about what Sharp takes from them.

• At Hampstead theatre, London, until 5 February