Whitty was born in at Sydney to Hamlyn Henry Whitty and his wife, Marguerite. He moved to England with his parents in December 1922, where he was educated at Clifton College. While at Clifton he was a member of the Clifton College contingent of the Officers' Training Corps. After leaving Clifton, he decided upon a career in the British Army, but was placed on the Supplementary Reserve, where he held the rank of second lieutenant. He accepted a commission into the Queen's Own Royal West Kent Regiment as a lieutenant in February 1931, having been on the Supplementary Reserve. In 1936, he made a single appearance in first-class cricket for the British Army cricket team against Cambridge University at Fenner's. Batting twice in the match, he was dismissed for a single run by John Cameron, while in their second-innings he was dismissed by the same bowler for 22. With the ball, he dismissed Allan White and John Pawle in the Cambridge first-innings, taking figures of 2 for 19, while in their second-innings he dismissed Norman Yardley and Hugh Bartlett, taking figures of 2 for 27. An all-round sportsman, beside playing cricket for the army, he also football, golf and rugby union for the army. He married Sheila Hope in 1937, with the couple having two children and residing at Seaford, Sussex. He was posted to Palestine on peacekeeping duties in 1938, where he saw action during the Arab Revolt. On 14 May 1938, he was slightly injured in a car accident during a night advance on Tamra. Despite this, he remained on the frontline and led an advance during the early afternoon on the same day. When he received word that a private was missing, Whitty, alongside captain Kelleher and private Parkin, searched for the missing private under heavy enemy fire and eventually found him, returning him safely to cover. For these actions he was awarded the Military Cross in August 1938. He was promoted to the rank of captain in February 1939.
At the outbreak of the Second World War, Whitty was sent to France with the British Expeditionary Force, as part of the 132nd Infantry Brigade. During the retreat to Dunkirk, he was wounded in the chest and shoulder. Shortly thereafter he was picked up by an ambulance and taken to a makeshift hospital in Dunkirk, before being evacuated to a hospital ship and returned to England, where he spent 21 days recovering from his wounds in hospital at Dover. Upon recovering, he was sent to North Africa, where he took part in the Battle of El Alamein. During his service in North Africa he was placed in command of the 5th within the West Kent Regiment, at which point he was promoted to the temporary rank of lieutenant colonel. He was described by Field Marshal Montgomery as "the best field commander in the Eighth Army". After North Africa he received further training, before taking part in the Italian Campaign. Within one month of being posted to Italy, he was awarded the Distinguished Service Order during an attack on Romagnoli in November 1943, in which he led from the front while being exposed to significant enemy fire. He was killed on 23 October 1944 when he stepped on a mine in the Italian town of Vicchio. He was buried at the Florence War Cemetery. Whitty was survived by his wife and their two children.
