Cokayne-Frith was born at St Stephen's House at Canterbury to Lieutenant Colonel Reginald Cokayne-Frith and his wife, Pauline.[1] He was educated at Eton College, before attending the Royal Military College, Sandhurst.[1]
He graduated from Sandhurst in the later stages of World War I as a second lieutenant, entering into the King's Royal Hussars and seeing action on the Western Front.[1] He was promoted to the temporary rank of lieutenant in December 1919,[2] with full promotion to the rank following in December 1921.[3] He was made an adjutant in April 1928,[4] and was shortly thereafter promoted to the rank of captain in July 1928.[5] He was again made an adjutant in September 1933, when he was seconded to the North Somerset Yeomanry.[6][7] He remained seconded to the North Somerset Yeomanry until November 1937,[8] returning to the King's Royal Hussars in January 1938.[9] He was promoted to the rank of major in August 1938.[10] He played a single first-class cricket match for the British Army cricket team against Cambridge University at Fenner's in 1939.[11] Batting once in the match, he scored 54 runs in the Army's first-innings, before being dismissed caught by George Mann off his brother John Mann's bowling.[12]
He served with the King's Royal Hussars during the Second World War, seeing action during the Battle of Belgium.[1] He was killed in a rearguard action on 18 May 1940, during the British Expeditionary Force's retreat to Dunkirk, when his tank was destroyed by a German anti-tank gun in the Belgian town of Assche.[1] He was the most senior member of his regiment to be killed on that day.[1] He was posthumously mentioned in dispatches for his actions throughout the retreat.[13]