Harvey was born in Glasgow. His musical roots were in Dixieland jazz and skiffle music, which were an inexplicable fad in England and Scotland during the late 1950s. During this period, he won a competition that sought "Scotland's answer to Tommy Steele," a rock star apparently better known then as a pinup than remembered today as a performer. Alex Harvey was literally the "last of the teenage idols," a distinction he made much of during his subsequent career.
In 1959, Harvey formed "Alex Harvey's Soul Band," and recorded blues and rock and roll material, to modest success. In 1966, Harvey found more success as a member of the cast in London production of the musical Hair.
In 1972, Harvey formed the Sensational Alex Harvey Band, composed of himself and the former members of a progressive rock band called "Tear Gas." It was with the Sensational Alex Harvey Band that Harvey had his greatest successes, both musical and sales. Harvey's skiffle background led him to include unusual material for the period in his sets, including old pop songs and Broadway musical material. His live act also usually featured a tale of "Vambo," an urban superhero who was the subject of some of his more energetic numbers.
The Sensational Alex Harvey Band scored chart hits in Britain with the single Delilah, a remake of the Tom Jones hit, and also with The Boston Tea Party.
Harvey died of a heart attack in Zeebrugge, Belgium, the day before his 47th birthday.