One of the most popular figures in British sporting history, Cooper was Amateur Boxing Association light-heavyweight champion in 1952 at the age of just seventeen. Picked to compete for Great Britain in the Helsinki Olympics he was defeated in his opening contest by the eventual bronze medallist, Perov of the USSR.

After retaining his national amateur championship in 1953 he turned professional the next year. After a period where he lost as many fights as he won Cooper's career flourished from the late fifties and he won both British and British Empire Heavyweight titles. In the summer of 1963 he was matched with the unbeaten 1960 Olympic light-heavyweight champion Cassius Clay. Clay had commented before the bout that "Henry Cooper is nothing to me! If this bum goes over five rounds, I won't return to the United States for 30 days, and that's final! I'm not even worried about this big bum Cooper will only be a warm-up until I get to that big ugly bear Sonny Liston!" Cooper's strongest weapon was his left hook, the press had labelled it "Enery's 'Ammer" (Cockney slang for Henry's Hammer) and at the end of round four it landed squarely on Clay's chin and the American fell to the canvas. Unfortunately for Cooper this came in the final seconds of the round and by the start of the next round Clay had recovered. The referee stopped the contest in the fifth round when Cooper's facial cuts became too bad to continue.

He rebounded to win the European title and three years after their initial contest he would step into the ring to face Clay, now under his new name of Muhammad Ali, this time for the world title. The second meeting ended as the first did with Cooper's face a bloody mess.

Although he would never again fight for a world title he defended his British, British Commonwealth and European titles until 1971 when he lost them all in his last professional bout. He held the British and British Empire/Commonwealth titles for twelve years between 1959 and 1971 and the European title on three separate occasions in the sixties and early seventies.

A small heavyweight who struggled against the top fighters in his division and his propensity to cut easily also hampered his career. On his retirement he became a popular television personality, appearing on the BBC quiz show "A Question of Sport" and also in adverts for aftershave. One of only three sportsmen to have won the BBC's Sports Personality of the Year award twice (1967 & 1970), in 2000 he became the first boxer to be awarded a knighthood.