The son of a bank manager from Essex who went on to become a missionary in Africa, Craft was a buyer of ladies underwear in his youth before becoming involved in motor racing through his brother Andrew, who owned a body shop in Woodford Green. He started racing in 1962 in a Ford Anglia and went on to race a variety of other touring cars until he tried his hand at single seaters in a Merlyn Formula 3 car. He was later hired by the Italian chassis company BWA but that was not a great success and he later switched to a Tecno. He also teamed up with Alain de Cadenet to race his Porsche 908 and Can-Am McLaren. In 1971 de Cadenet bought an ex-works Brabham BT33 which Chris drove in the US Grand Prix at Watkins Glen. He continued to race into the 1980s, while also acting as the assistant competition manager for Ford and running a used car business, before he raced on in saloon and sports cars right through to the early 1980s. In recent years he has run an engineering business called the Light Car Company.