Cooper was twice voted BBC Sports Personality of the Year and, after retiring in 1971 following a controversial loss to Joe Bugner, remained a popular public figure.

Cooper took up many jobs, including a paper round before school, and made money out of recycling golf balls to the clubhouse on the Beckenham course.

[3] Wicks had a reputation for not overmatching his boxers and looking out for their interests; however, the very cut-prone Cooper was slow to fulfil his potential and early title challenges were unsuccessful, with losses to West Indian Joe Bygraves for the Commonwealth belt (KO 9), Ingemar Johansson for the European belt (KO 5), and the undersized but highly skilled Joe Erskine (PTS 15) for the British and Commonwealth.

Another points win over London brought an offer to fight Floyd Patterson for his world heavyweight title, but this was turned down by Cooper (or Wicks).

[3] In 1963 Muhammad Ali (then known as Cassius Clay and a contender for the world heavyweight title) created a great deal of ticket-selling publicity before his London bout with Cooper, who many British fans hoped would be able to humble the brash young American.

A stiff connection by Ali split open the face of Cooper in the middle of round three, beginning a gush of blood into his left eye.

Cooper insisted that resulted in a delay of a minute or more in addition to the regulation time between rounds, and denied him a chance to finish off Ali while he was still dazed.

[7] Ali started the 5th round aggressively, attempting to make good his prediction of a 5th-round knockout and opened a severe cut under Cooper's eye.

[7] After a fourth-round knockout loss to former world heavyweight champion Floyd Patterson in 1966, Cooper went undefeated until the final contest of his career.

In 1970, Cooper would vacate his British Heavyweight Title after attempting to arrange a fight with World Boxing Association champion, Jimmy Ellis.

Referee Harry Gibbs awarded the fight to Bugner by a quarter of a point score (which was subsequently abolished partly because of the controversy that followed).

An audience mainly composed of Cooper fans did not appreciate the innately cautious Bugner, and the decision was booed with commentator Harry Carpenter asking, "And how, in the world, can you take away the man's three titles, like that?

[16] In the 1960s Cooper appeared in several public information films concerning road safety, promoting the use of zebra crossings: such as "The Story of Elsie Billing".

[17] After his retirement from boxing, he maintained a public profile with appearances in the BBC quiz show A Question of Sport and various advertisements, most famously in those for Brut aftershave.

[18] He appeared as boxer John Gully in the 1975 film Royal Flash and in his latter years featured in a series of UK public service announcements urging vulnerable groups to go to their doctors for vaccination against influenza called Get your Jab in First!

[15] Subsequently, Cooper's popularity as an after dinner speaker provided a source of income, and he was in most respects a picture of contentment although becoming more subdued in the years following his wife's sudden death aged 71.

[15][18] Considering his long career, Cooper had suffered relatively little boxing-related damage to his health, and apart from "a bit of arthritis" remained an imposing figure: in the words of one journalist, "the living manifestation of an age of tuxedos in ringside seats, Harry Carpenter commentaries, sponge buckets and 'seconds out'".

[3][20] He converted to her Catholic faith and described Albina, who "hated" his sport, as "an ideal wife for a boxer", never grumbling about his long absences before big fights and inviting journalists in for tea while they waited for Cooper to get out of bed the morning after bouts.