It's her voice that grabs your attention. Light but earthy, vulnerable but calm, Anne Briggs's voice is unique. Without changing the way she sings, she can convey a father's barely-concealed hots for his daughter's boyfriend ('Willie O'Winsbury'), the desolation of a girl promising her dead lover in a dream that she'll cut off her hair so that nobody else will want her ('Lowlands'), or a new bride's hilarious contempt for her elderly husband's inability to perform ('The Whirly Whorl'.) It's the voice that earned her the admiration of the likes of Sandy Denny, Bert Jansch, June Tabor, Maddy Prior, Richard Thompson, The Decembrists and, basically, anyone who has ever heard her sing.

Between 1963 and 1971, Nottinghamshire singer Anne Briggs made a handful of recordings, a mere 33 songs, which comprise one of the most brilliant legacies in folk music. She was also one of the most notorious wild kids on the British folk scene, almost as renowned for her heroic alcohol consumption as for her skill and her impeccable choice of repertoire (Richard Thompson went to see her twice back in the day, and on both occasions he got there in time to find her passed out from drink.) The glamour of the young Briggs is captured in contemporary pictures of her, in which she looks like Charlotte Gainsbourg's sulky, baggy-sweater-wearing younger sister. Her second album The Time Has Come was the first to feature mostly her own songs, but good as it is, it's eclipsed by her earlier recordings for Topic Records: the 1963 EPs The Iron Muse and The Hazards of Love and the 1971 debut album Anne Briggs, all of which are available as a single CD. (The eight-year gap between Briggs's first recordings and her debut album incidentally demonstrates how much of a sensible careerist she was.) She recorded a third album in 1973, Sing A Song For You, but it wasn't released until 1997, reportedly because she disliked her own singing.

After 1971, nothing more was heard from Briggs. She didn't die or go crazy, she just stopped enjoying the work of being a musician and decided to do something else with her life: she worked in forestry conservation, she ran a 'bunkhouse and tea garden', and she raised her kids. She's steered clear of the music industry for four decades, although in the last few years the ongoing interest in her career has caused her to pop up in brief TV and newspaper interviews, in which she comes across as friendly, sensible and rather baffled by all the fuss. On Sunday 31 Jan she's making a very rare appearance at the Glasgow Film Theatre, to be interviewed by writer and broadcaster Pete Paphides as part of Celtic Connections. The interview will be followed by a screening of Acoustic Routes, a documentary about the 60s folk scene.

It's not a criticism to say of Briggs's contemporaries Vashti Bunyan and Sandy Denny that, like most singers, they throw a good deal of personal attitude into their singing. Bunyan has her little-girl-lost quiver, Denny had that brimming sense of drama that made her such an appropriate guest performer on Led Zeppelin IV. But Briggs's attitude is to project no attitude at all. Her voice is as mysterious and as inexplicably moving as the sea, or the sky. If she isn't better known, it's partly because she likes it that way. She famously doesn't like cities – one reason she isn't more famous is that she used to be uncomfortable singing indoors, for God's sake – so make her feel welcome, Glasgow.

Anne Briggs is in conversation with Pete Paphides at the Glasgow Film Theatre at 2.30pm on Sun 31 Jan.