Winstone played piano and organ in her youth. She began singing semi-professionally by the age of 17, influenced by conventional jazz vocalists. During the '60s she became attracted to the jazz avant-garde. She played in groups led by pianists Michael Garrick and Mike Westbrook; she also sang with such forward-thinking musicians as saxophonist John Surman, flügelhornist Kenny Wheeler, composer Michael Gibbs, and pianist John Taylor (whom she married in 1972). A late-'60s gig at Ronnie Scott's club in London (also on the bill was the legendary tenor saxophonist Roland Kirk) garnered her critical notice. In 1971 she was named best jazz singer in a poll by the British publication Melody Maker. That year, she recorded her first album as leader, Edge of Time, for the Decca label. With Wheeler and Taylor, Winstone formed Azimuth, a critically acclaimed contemporary chamber jazz group that recorded several times for the ECM label starting in the mid-'70s. Winstone is also an accomplished lyricist, having written words to music composed by guitarists Egberto Gismonti and Ralph Towner, bassist Steve Swallow, and vocalist Ivan Lins, among others.

Winstone has also performed and/or recorded in ensembles with Jimmy Rowles, Lee Konitz, Tony Coe, Fred Hersch, John Abercrombie, Dave Holland, Peter Erskine, and George Mraz. In 1992 she collaborated with composer/arranger Steve Gray in the creation of "A French Folk Song Suite," commissioned and performed by the North German Radio big band. She is also a member of Wheeler's big band. In July 2002 she was awarded the title Best Vocalist at the BBC Jazz Awards at London's Queen Elizabeth Hall.