The heavyweight was best known for knocking down a young Cassius Clay in 1963, in a fight which many commentators believed he should have won.
He floored Ali in the fourth round with "Enry's Ammer" - his trademark left hook - but Ali was given the chance to recover when his corner claimed he needed to change his ripped gloves. Ali eventually won the non-title fight at Wembley, with Cooper bleeding, as was common in his fights, around the eyes. Ali triumphed again when they boxed three years later but Cooper remained a favourite with the British public. In 1970, Sir Henry become the British, Commonwealth and European heavyweight champion, and cemented his reputation as one of the greatest post-war home-grown boxers. He remains the only boxer to have won three Lonsdale belts outright. He was knighted in 2000.
Robert Smith, the general secretary of the British Boxing Board of Control, paid tribute to Cooper tonight and described him as "one of the sporting icons, not just for the boxing public but sport in general".
Speaking to Sky Sports News, Smith continued: "He fought Muhammad Ali twice, once when he was Cassius Clay and once when he was Muhammad Ali, and he put up wonderful performances.
"Ali is possibly the greatest athlete there's ever been and Henry put up a great performance and just wasn't quite good enough on both occasions - but he's not the only one who wasn't good enough to beat Ali.
"Ali was one of the first 'big' heavyweights and Henry lost to Joe Bugner, who was 15-odd stone and Henry was 14 - just bigger men. For such a small man, he put up some great performances in a world-class context."
On the affection in which Cooper was held, he added: "It's not just the boxing and your ability, it's the personality as well.
"He won the BBC Sports Personality of the Year on two occasions, which is a tremendous feat for a boxer. Everyone called him 'Our Enry', and he was much loved, he served boxing wonderfully."