Cotton was encouraged to play golf by his father, and after being coached by J.H. Taylor he became a full-time professional golfer in 1926. His first win of the British Open in 1934 ended a decade of American victories in that major tournament. He won the British Open again in 1937 and 1948. He also won 11 European Open championships, and he represented Great Britain in Ryder Cup competition four times.

Conspicuously ambitious and intelligent, Cotton was a compelling personality who contributed enormously to elevating the status of the professional golfer in Great Britain. After his retirement he taught and wrote numerous books and articles on golf, including Studying the Golf Game (1964), A History of Golf (1973), and Thanks for the Game (1980). He was awarded a knighthood posthumously.