Buckley rose to fame on I'd Do Anything, a talent show seeking an actress to play Nancy in a West End production of Oliver!.
She gave an interview to British Vogue in January talking about how she was criticised for her appearance.
"I don't like that part of it," she told Laverne. "I think that was a young woman who's trying to discover her body and herself, like we all do. And I wish that hadn't happened.
"I was putting a brave face on, because really what I wanted to do was sing and I wanted to act, and I wanted to be part of this industry, and all of a sudden you had to be a certain kind of person.
"And I just wasn't, I never will be. That's just not me."
Buckley sounded emotional as she chose a rendition of her mother, Marina, singing O Holy Night in church as one of her tracks.
"My parents are no longer together, and she lives in Dublin, and she's writing her own story right now at 60 years of age," Buckley said, "and I'm so proud of her."
Jessie Buckley's Desert Island Disc choices:
Disc one: Samhradh Samhradh - The Gloaming
Disc two: O Holy Night. Composed by Adolph Adam and performed by Marina Cassidy
Disc three: Who Knows Where the Time Goes (Live at Philharmonic Hall, New York, NY - October 1969) - Nina Simone
Disc four: Troy - Sinéad O'Connor
Disc five: Send In the Clowns – Judi Dench
Disc six: Shobis Galoba (Christmas Song) - Basiani Ensemble
Disc seven: The Red Shoes - Kate Bush
Disc eight: Old Note - Lisa O'Neill
Book choice: The Complete Poems of Tim Buckley
Luxury item: Jessie's own bathtub and bath salts
Castaway's favourite: Samhradh Samhradh - The Gloaming
From BBC
Darryl Preston said the event was about "building trust" with communities
