McKenzie started his career in 1970 as a member of the Global Village Trucking Company who all lived together in a Norfolk commune with their families, and become a well known live act by playing extended jams at numerous benefit concerts and free festivals. Their first recording was as part of Greasy Truckers Live at Dingwalls Dance Hall, a benefit album released in 1973. The same year, the BBC made and broadcast a documentary about the band, their commune and their shunning of record companies. In 2008 the BBC made a follow-up documentary for their What Happened Next series, which included the band performing a re-union gig, their first in over 30 years, which led to Global Village gigs at Glastonbury 2008 and other festivals. In 1975 they recorded an eponymous album, but broke up shortly afterwards.
McKenzie came to prominence as the bass player of the rock band Man, which he joined in 1975, having had to audition for the role. He recorded The Welsh Connection for which he also wrote one track, and which reached No 40 in the UK Album Chart. During a US tour to promote the album, including performances with John Cipollina, in July/August 2006, differences between the band members arose, and on the next European tour McKenzie and Phil Ryan announced they would be leaving. However they remained together for a farewell tour, on which a live album. All's Well That Ends Well was recorded at the Roundhouse in December 1976.