During his playing career, he gained caps for England U21s (scoring five times) and earned a single full cap for the England team against Iceland in June 1982 (scoring once). In his fifteen-year career as a centre forward, he played for Queens Park Rangers, West Ham United, Newcastle United, Derby County, Millwall and Ipswich Town.
Goddard was capped once for England at senior level, on 2 June 1982, a 1–1 friendly draw against Iceland, during which he scored England's only goal. The game was originally an England B fixture but was subsequently upgraded to full international status meaning Goddard was awarded his cap. Despite this successful appearance, he was not selected for the World Cup squad that summer and never played a senior match for England again.