Arundell began his racing career in the British Formula Junior, which he won in 1962. In 1963 he drove in Formula 2 and in the British Formula 3 Championship, where he was champion in the same year. He then moved to Formula 1 and completed a total of eleven Formula 1 race in the seasons 1964 and 1966 for the Lotus team.
His best results were two third places, which he reached directly in his first two races at the 1964 Monaco Grand Prix and the Grand Prix of the Netherlands. This performance was only broken in 2007 by Lewis Hamilton, who finished the first nine Grand Prix races on the podium. Until his last Formula 1 race at the Grand Prix of Mexico in 1966, Peter Arundell could learn a total of twelve championship points.