The son of a biology teacher, Tebbutt served most of his time as a claiming rider with Chris Thornton at Middleham before moving to Newmarket where he saw out his apprenticeship with Willie Jarvis. He also rode on the gallops for Lester Piggott who, by then, had turned to training. Jarvis is still one of his main employers, along with Michael Jarvis, who is no relation to Willie, and Ed Dunlop.