Unfortunately for them, the link between Cheeseman and the Sussex body existed only in the minds of journalists. Far from being a headless corpse, he was sunning himself next to a swimming pool in Tenerife at the time.
Cheeseman's guilty plea in the United States federal court in Manhattan on Wednesday may have been less satisfying but it brought with it the prospect of a 55-year maximum jail sentence for the British fraudster.
Following his extradition from Spain, Cheeseman, 50, of Bethnal Green, east London, pleaded guilty to six criminal charges involving a conspiracy to sell more than dollars 550m ( pounds 392m) in stolen securities, including pounds 292m of bonds stolen at knifepoint in the City of London in May 1990.
The robbery, dubbed the world's biggest mugging, was initially believed to be the work of a small-time thief. Detectives in the City of London soon learnt that far from being a 'lucky' mugging, it was part of an international fraud and money-laundering ring, with organised crime links in the United States.
Two months after the securities were stolen, Mark Osborne, a Texan businessman, attempted to sell some of them to an undercover FBI agent posing as a narcotics dealer in New York. He was arrested, 'turned' and used to trap other members of the gang, including Cheeseman.
The bonds had been fenced all over the world. In the months after the robbery, detectives tracked down all but pounds 2m of the pounds 292m stolen. They arrested 25 people but only Cheeseman has ever been successfully prosecuted.
Cheeseman admitted receiving and handling dollars 23m ( pounds 16m) of stolen bonds. In return, he has requested that he serve his sentence in a British prison.
He is certainly familiar with Her Majesty's prisons. In 1977 he was jailed for six years for defrauding a US finance company by making bogus loan applications. The money was used to propel Cheeseman and Dunstable Town Football Club from amateur obscurity to national headlines. Cheeseman audaciously signed former Manchester United and Northern Ireland star George Best.
Attendances soared and success seemed assured. Cheeseman lived the high life and the champagne flowed until he disappeared suddenly, leaving thousands of pounds of debts in his wake.
After he was jailed the football club was forced into liquidation. He celebrated his release from Wormwood Scrubs, west London, in 1981 with champagne and was soon back to his old habits. He was back in jail in 1983 for three years after being found guilty of duping a bank manager and obtaining money by deception.
His involvement in the international bond racket came about shortly after his release from that sentence. He told friends that his new-found wealth stemmed from 'sound investments'. Police thought otherwise. And in November 1990 Cheeseman was arrested at his luxury flat in the Barbican, central London.
He jumped bail and fled to Tenerife - where he was recaptured and extradited to the US. He claims that he fled because he feared a Mafia godfather had put a contract out on him and a hit- man was closing in.
His fellow conspirator, Mark Osborne, was murdered. His body was found in the boot of a car parked in Houston, Texas. Osborne had been shot twice in the back of the head. His family is now suing the FBI for allegedly failing to protect him.
Cheeseman, who also faces up to dollars 1.5bn ( pounds 1.1bn) in fines, will be sentenced next month.
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