Mid-1960s was Burrell singers " The Boz People". During this time he replaced briefly Roger Daltrey of The Who.
In the late 1960s he published as a singer under the name Boz solo singles. He was accompanied by Ritchie Blackmore, Ian Paice and Jon Lord, Deep Purple founded shortly thereafter. He also sang on Keith Tippett Album Septober Energy.
In the early 1970s rose Burell King Crimson as a singer and bass player. In 1971 he played the Islands album and the live album Earthbound. 1973 Burrell founded the band snap with members of King Crimson and Alexis Korner's band.
In 1973 he became a founding member of Bad Company. Until 1999 he remained in the band.
After leaving Bad Company Burrell worked with Tam White and in the 2000s with Zoot Money's Big Roll Band. In 2006 he died at age 60 of a heart attack in Spain.