- Chairman of the Variety Club of Great Britain's Golf Society.
- Had done his National Service with the 4 Battalion, Royal Army Ordnance Corps.
- Former European and British and Commonwealth heavyweight boxing champion. He fought Muhammad Ali twice. His left-hook was nicknamed 'Henry's Hammer'.
- Had a twin brother, George Cooper, also a professional boxer under the name Jim Cooper. Henry was the elder by 20 minutes.
- He was awarded the OBE (Officer of the Order of the British Empire) in the 1969 Queen's Honours List before being awarded Knight Bachelor of the Order of the British Empire in the 2000 Queen's New Years Honours List for his services to Boxing.
- One of only four men who ever knocked down Muhammad Ali. The others were Sonny Banks, Joe Frazier and Chuck Wepner.
- Officially opened the Britannia Park theme park (later to be renamed the American Adventure theme park) in Ilkeston, Derbyshire, England.
- He was also celebrated as one of the great Londoners in the "London Song" by Ray Davies on his album "The Storyteller" (1998).
- Challenged John Grigg to a boxing match after Grigg wrote an article seen by Cooper and others as a personal attack on Queen Elizabeth. Grigg wrote that her "tweedy" courtiers made her come across in public as "a priggish school girl" with speaking style he described as "a pain in the neck" [1957].
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