Goddard was born in Croydon, London, England, in 1962. Between 1974 and 1979, he attended Ravensbourne School, Hayes Lane, Bromley, London. A punk in 1977, he helped form a band at school called The Belsen Horrors (the name of which came from a Sex Pistols track). First a Drummer, then the lead singer, he and his band lasted until 1978. Later, sometime between 1979 and 1980, he was the Drummer in another Bromley punk band called The Vamp. This group was led by Wayne Cregan, who was one of the first members of X-Ray Spex. Bromley was closely linked with the early punk movement – first through the Bromley Contingent (the first fans of the Sex Pistols), and three famous punk Singers who came from this town: Poly Styrene (X-Ray Spex), Siouxsie Sioux (of Siouxsie and the Banshees) and Billy Idol – who like Trevor, attended Ravensbourne School for Boys.