Around 1942, their father, Henry Senior was called up to serve in the war; the rest of the family would not see him again for almost three years. The twins would attend Athelney Road School in Lewisham. The Cooper brothers were particularly close growing up and in his biography, Henry talks of how they would come to each other’s aid when things turned nasty in the school playground. One particular incident would land the young Henry his first knockout in the playground. At school, the only subject that seemed to interest Henry was history where he had the enjoyment of acting out scenarios.

Life was tough in the latter years of the Second World War, and especially in London, urban life brought many dangers during the blackout. Henry had to take up many jobs including a paper round before school and even making money out of recycling to the clubhouse golf balls on the Beckenham course. All three of the Cooper brothers were known to excel in sport with George and Henry exercising talents particularly in football and also cricket.

Early bouts
Cooper is often regarded as the most popular of all English boxers and affectionately known in England as: "Our 'Enry". He was at one time the British, European and Commonwealth heavyweight champion. His early title challenges were unsuccessful, losing to Ingemar Johansson for the European belt (KO 5) and Joe Erskine (PTS 15) for the British and Commonwealth. He then won on points over highly rated contender Zora Folley and took the British and Commonwealth belts from new champion Brian London in a 15 round decision. The winner of the fight was pencilled in to get a shot at Floyd Patterson's heavyweight title, but Cooper turned down the chance and London went instead. Cooper continued to defend his British and Commonwealth belts against all comers including Dick Richardson (KO 5), Joe Erskine (TKO 5 and TKO 12), Johnny Prescott (TKO 10) and Brian London again (PTS 15), although he suffered a setback when losing a rematch with Folley by a second round KO. Cooper was also offered a chance to fight Sonny Liston but his manager Jim Wicks rejected the idea, saying "If we saw Sonny Liston coming, we’d quickly cross the street."

Fights with Cassius Clay
Cooper fought Cassius Clay twice, firstly in a non-title fight in 1963 at Wembley Stadium, when Cooper knocked Clay down in the fourth round with his trademark left hook, "Enry's 'Ammer". The bell rang before Cooper could try to complete a knockout. Prior to the fight Clay's trainer Angelo Dundee had noticed a small tear in one of Clay's gloves but didn't bring it to the referee's attention. With Clay now staggered from the knock down, Dundee opened up the tear with his finger and told the referee that his fighter needed a new pair of gloves, thus delaying the start of the 5th round.[2] Cooper has always insisted that this delay lasted anywhere from 3-5 minutes and denied him the chance to try to knock Clay out while he was still dazed. When the 5th round finally started, Clay ferociously attacked Cooper's cuts, leaving Cooper's face streaming with blood and referee Tommy Little was forced to stop the fight in the American's favour.

The British boxing newspaper Boxing News conducted an investigation into the 'split glove' incident in 2003. Using the original television and radio broadcasts to determine length of time between rounds 4 and 5 it was discovered that Cassius Clay only gained 5 seconds extra and not the mythical 3-5 minutes. The gloves were never changed. Other sources on the matter confirm this.[3] [4] After this fight a spare pair of gloves were always required at ringside. What is certain however, is that Dundee broke a file containing an unknown substance and held it under Clay's nose in an effort to revive his man, which was illegal.[5] Clay was obviously impressed by the knockdown and on the 40th anniversary telephoned Cooper to reminisce. Clay who had changed his name to Muhammad Ali in 1964, later said, on British television, that Cooper "had hit [him] so hard that his ancestors in Africa felt it". In 1966 they met a second time to contest the world title. Cooper succumbed again to his weakness, a tendency to cut, and Ali went on to be "The Greatest".

Last fights
After the loss to Clay, Cooper fought former heavyweight champion Floyd Patterson. Cooper lost by a 4th round knock out. After that he went undefeated until the final fight of his career. In 1968 Cooper added the European crown to his domestic titles with a win over Karl Mildenberger making 2 successful defenses. In his last fight he faced the emerging British heavyweight hope Joe Bugner in 1971 for the British, European and Commonwealth belts. Fight referee Harry Gibbs awarded the fight to Bugner by the narrowest of margins: a quarter of a point. Many felt that defeating the popular Cooper was one reason why British fans didn't take to Bugner. The decision was booed by the audience, which was mainly composed of Cooper's fans. Commentator Harry Carpenter, asked how "they can take away the man's titles like this?" However, one commentator felt the younger, stronger Bugner had done enough to win.[6] Cooper announced his retirement shortly afterwards. For years after the fight, Cooper refused to speak to Gibbs. Cooper has since stated: "I didn't speak to him for years after the fight. I don't usually hold grudges, but I knew certain things went on before the fight (that I don't want to speak about) and for those reasons I didn't speak to him until about six months before he died." Cooper eventually agreed to shake his hand for charity.[7]

Alongside figures such as Frank Bruno, Bob Fitzsimmons, Joe Bugner, Tommy Farr and Lennox Lewis, Cooper is regarded as one of the all-time best British heavyweights.

Cooper was given the award in 1967 for going unbeaten throughout the year. One of the most memorable fights of the year was his defeat of challenger Jack Bodell in June.

His second award came in 1970, when Cooper had become the British, Commonwealth and European heavyweight champion, cementing his reputation as one of the greatest post-war British boxers.