Goffe began his racing career in 1934 at the sand track in the resort of California near Wokingham, riding for prize money.[3][4] He then concentrated on grasstrack racing, winning the South of England Grass Track Championship at Basingstoke in 1936.[3] He bought a 500cc Rudge bike from "Froggy" French in 1936, which he used in his early speedway rides, impressing sufficiently to receive offers from both Hackney Wick Wolves and the Johnny Hoskins-managed West Ham Hammers, signing for the latter in 1937.[3][4] He had a brief spell with the Leicester Hounds team, riding in three matches in 1937 before the club withdrew from the Provincial League.[5]
His performances progressed after transferring to the Harringay Tigers later that season, staying with the team until the outbreak of World War II.[3] During the war, he served as a fitter in the Royal Air Force.[4]
After the end of the war, Goffe joined the Wimbledon Dons in 1946. His riding style led to him being nicknamed "Cowboy".[4] He achieved one of his ambitions in 1946 by beating the Wembley captain Bill Kitchen in a race.[6] In 1948 Goffe rejoined Harringay (now the 'Racers') for a £1,350 transfer fee,[5] where he won the Anniversary Cup in 1949 and by 1950 his career completed a full circle when he rejoined West Ham.[7]