Whitney attended Leicester Art College in 1962, and he formed his own band known as The Farinas. They played rhythm and blues, and featured Jim King on saxophone and vocals, bassist Tim Kirchin and drummer Harry Overnall. They performed songs by Chuck Berry and The Coasters before releasing the single "You'd Better Stop" in August 1964. Later, Ric Grech replaced Tim Kirchin and Roger Chapman joined as the principal lead singer, giving a heavier blues sound before renaming the band The Roaring Sixties.
During 1966, The Roaring Sixties were renamed Family and they replaced their drummer Overnall with Rob Townsend. The band issued its first single as Family entitled "Scene Through The Eye Of A Lens/Gypsy Woman" in 1967 and Family's debut album Music in a Doll's House followed in July 1968. Family's heavy, experimental rock music gained them a reputation as a progressive underground band. By 1970, with the release of their albums A Song For Me and Anyway and an appearance at the third Isle of Wight Festival on 28 August 1970, Family was creating some of the fastest and loudest rock and the most intense acoustic music in the British underground scene. Although Family proved to be popular in UK and continental Europe, success in the US eluded them and in 1973 the group broke up.
Whitney's angular guitar passages on songs like "Drowned In Wine" and "Good News Bad News" were singled out by fans and critics as being essential to the Family sound. He and Chapman wrote most of Family's songs together as a team. Whitney also composed two tracks, the instrumental "Summer '67" and the childlike folk song "Processions", about a small boy enjoying a day at the seashore.
Whitney formed Streetwalkers with Chapman in 1973. This new band included vocalist and guitarist Bobby Tench, from The Jeff Beck Group and Hummingbird, and future Iron Maiden drummer Nicko McBrain. They signed to the Vertigo label as Chapman Whitney Streetwalkers, recording an album entitled Streetwalkers (1974), with a line-up including other members from Family and King Crimson. Chapman and Whitney morphed their band into the Streetwalkers, which comprised five members including Bobby Tench, drummer Nicko McBrain—who later moved on to play with Pat Travers (and eventually Iron Maiden)—and bassist Jon Plotel. The band broke up in 1977, ending eleven years of the Whitney-Chapman musical partnership.
Whitney remained active in rock music. He reunited with Rob Townsend, his bandmate from Family, to form Axis Point in 1978. The line-up for this band included piano player Eddie Hardin, vocalist and guitarist Bobby Tench from Streetwalkers and former Taste bassist Richard McCracken. When Axis Point broke up in 1980, Whitney formed Los Racketeeros, a live unit which played blues and bluegrass music. Los Racketeeros recorded a debut album in 1995 with a line-up including Alan Rogers, Pete Tomlyn, and Tony Taylor. Whitney released a solo album in 1999, and played concerts with Robert A. Roberts, a singer-songwriter, vocalist, harmonica player and guitarist, who had been a founding member of the London Bluesband Roadhouse. They released a CD as The Whitney-Roberts Combo experimenting with folk music.