Leslie Garrett was born in the town of Thorne, near Doncaster, South Yorkshire into a musical family. She attended Thorne Fieldside Infant and Junior Schools and Thorne Grammar School, where she performed in school plays and musicals and passed 10 O-levels and an A-level in music. As she grew up she inherited her family's love of music. Her grandfather Colin Wall was a classical pianist; her father Derek worked as a railway signalman and then as a schoolteacher at Hatfield Woodhouse Primary School, eventually going on to become a headmaster. They lived nearby just south of the village; her mother Margaret (née Wall) was a talented singing seamstress and became the school secretary at Lesley's primary school. She has two sisters, Jill and Kay, one step-sister, Louise, and two step-brothers named Robert and Nicholas. When Lesley was 17 she washed dishes at the officers' mess at nearby RAF Lindholme as a summer job. While a student at the Royal Academy of Music she worked as a life model, something of which she is still proud.

Garrett has had an extensive music career. A graduate of the Royal Academy of Music and an alumna of the prestigious National Opera Studio, she won the Decca Prize of the Kathleen Ferrier Award in 1979, thereby launching her career. Her professional debut, in 1979, was as Amor in Orontea at the music festival in Batignano. She subsequently sang, in 1980, Alice in Le comte Ory at the London Coliseum and Dorinda in Orlando at the Wexford Festival, in 1981, also at Wexford, the title role in Zaide, in 1982 Sophie in Werther with Opera North and in 1984 Damigella in L'incoronazione di Poppea at Glyndebourne. From 1984, as principal soprano at English National Opera, she became well known for her performances in productions of the operas Serse, Le Nozze di Figaro, Così fan tutte and Die Fledermaus.

Garrett has performed across the world, in countries throughout Europe, and also the United States, Australia, Russia, Brazil, Japan, Malaysia, Taiwan and South Korea. She has also sung opera and pop classics with Bryan Ferry, Eurythmics and Mick Hucknall to celebrate the arrival of the new century on Millennium Eve in the grounds at the Royal Observatory and National Maritime Museum.

She played the lead role of Hanna Glawari in the Welsh National Opera's production of The Merry Widow, which toured the United Kingdom in 2005. In 2006 she sang the role of Mother Abbess in Andrew Lloyd Webber's revival of The Sound of Music. In 2008, she joined the cast of Carousel as Nettie Fowler. The production toured the UK and then transferred to the West End's Savoy Theatre. In 2013 she returned to opera with the monodrama La Voix humaine for Opera North.

She created the role of Val in Pleasure, the first opera by Mark Simpson, directed by Tim Albery and premiered at the Howard Assembly Room by Opera North, in April 2016.

Garrett is a member of the board of the English National Opera and a vice president of Harrogate International Festivals.

In 2002 Garrett was appointed a CBE for her services to music. She was also awarded with a BASCA Gold Badge Award in October 2010, in recognition of her contribution to music.