Up in weight

His next three fights, at heavyweight, were all won by technical knockouts. The third one was against the Welshman, Tommy Farr, who had been an excellent heavyweight, fighting against the great Joe Louis, but who was now at the end of his career, and had aged quite a bit.

The fight against Farr was a final eliminator for the British heavyweight title, and so put Cockell in line for a title challenge against the holder Johnny Williams. The bout for the British and Commonwealth titles was held at Harringay Arena on 12 May 1953, and Cockell won on points over fifteen rounds.

Cockell then had two more wins before defending his Commonwealth title against Johnny Arthur in Johannesburg, South Africa. He won the fight on points after fifteen rounds.

Cockell moved rapidly up the heavyweight rankings by scoring three wins against American fighters. First he beat Roland La Starza on points at Earls Court Arena, then he had successive victories over Harry (Kid) Matthews, first at the White City Stadium and then at Sicks' Stadium, Seattle.

These victories put him in line for a title fight against undefeated heavyweight world champion Rocky Marciano. This was the first British world title bid since Tommy Farr had fought Joe Louis in 1937.

World heavyweight title fight

On 16 May 1955, Cockell fought Marciano for the world heavyweight title at Kezar Stadium in San Francisco, CA. Cockell was a 10–1 underdog and weighed 14 st 9 lbs against Marciano's 13 st 7 lbs, coming into the fight weighing 205 pounds to Rocky's 189. For the first three rounds the fight was fairly even, but as it progressed further Cockell began to take more and more punishment, without being able to hurt Marciano much. Cockell ended the eighth round hanging through the ropes after withstanding a terrific beating. Marciano won the fight by a technical knockout 54 seconds into round nine after Cockell had been knocked down twice, for counts of eight and seven. After the fight, Marciano stated, "He's got a lot of guts. I don't think I ever hit anyone else any more often or harder."

Many boxing fans in Britain felt that Marciano employed unfair tactics, such as hitting after the bell and low punches, but although the British Boxing Board of Control protested, Cockell himself made no complaints.

In covering the fight for Sports Illustrated, Budd Schulberg wrote in the 30 May 1955 edition, "Except for the technicality of wearing eight-ounce gloves, Don Cockell's stand against Rocky Marciano in the fading daylight hours of a cool San Francisco sunlit day was a glorious—or appalling—throwback to this pre-Marquess of Queensberry condition. This was a bare-knuckle brawl with gloves—and not a pleasant sight either—as an uncouth, merciless, uncontrolled and truly vicious fighter (the unbeaten Champion Marciano) wore down an ox-legged, resolute fat man who came into the ring with the honor of the British Empire weighing heavily—and consciously—on his massive, blubbery shoulders. He had promised his Union Jack supporters that he would not let them down, and the first words he mumbled through swollen lips after his fearful beating in nine rounds were an apology to his fellow countrymen for not having done better."

Jack Gallagher of the Oakland Tribune praised Cockell's brave effort, writing, "The fight was all Rocky's from the beginning. The Englishman showed amazing capacity for soaking up punishment."

Aftermath

The title fight had taken much out of Cockell, and he lost his subsequent two fights. In September 1955 he lost to the Cuban contender Nino Valdes at the White City Stadium by a technical knockout in the third round. He weighed 15 st 6 lbs for the fight. In April 1956 he was knocked out in the second round by Kitione Lave, known as the "Tongan Terror". That was his final fight. In May 1956 he was stripped of his Commonwealth title and in July he surrendered his British title and declared his retirement.

Cockell sued the Daily Mail after the newspaper had described him as being 'overweight and flabby' for his last fight, and not giving his all. He received £7,500 damages with costs.

Fight record

He had 81 official fights, winning 66, of which 38 were by knockouts, and lost 14, with one drawn fight.