His family, all socialists, had been accused of plotting to murder the prime minister, Lloyd George. His mother, sister and brother-in-law were sentenced to long terms of imprisonment for the supposed plot, now regarded by historians as an elaborate sham set up by the security services.
Wheeldon, on the run from the military authorites for refusing the call-up, was never charged.
Yet, instead of settling down to life in his ideal society, Wheeldon was arrested by Stalin's secret police and was shot in a labour camp.
Two weeks ago, the Russian security ministry, successor to the KGB, named a man they said was a British Communist sympathiser who had been arrested, sentenced to death and shot. The name given by the Russians was misspelt as William 'Wileden'.
Wheeldon was identified last week by Nick Hiley, a Cambridge historian. Dr Hiley, who has studied the period and been given access to closed papers in Home Office files, has pieced together the events of Wheeldon's life in Britain up to his departure for Russia in 1921, at the age of 29.
'He was an idealistic young man who suddenly found himself in the middle of dramatic historical events,' Dr Hiley said. 'There is a terrible irony in that he left Britain to escape persecution and begin a new life, only to be shot.'
Wheeldon was born in 1892 into a radical family. His mother, Alice, was an early socialist, feminist and a suffragette. His sisters, Nellie, Hettie and Winnie, were educated and politically active. William - 'Willie' - was an anarcho-syndicalist, a member of the Socialist Labour Party, and opposed to Britain's participation in the First World War.
It was Willie's decision in 1916 to refuse the call-up that set in train events that led to his family being tried for conspiracy to murder at the Old Bailey, apparently framed by the security service, MI5. The case became a socialist cause celebre.
In the fervently pro-war atmosphere of the day, Wheeldon, a member of the No-Conscription Fellowship, lost his job as a teacher in Derby, where his mother ran a second-hand clothes shop. His claims to be a conscientious objector were rejected and he eventually went into hiding with other anti-war protesters.
By late 1916 he had found his way to an 'underground' of Quakers, who moved anti-war protesters in secret from house to house to evade arrest. MI5, then in its infancy, took an interest in the network as part of its trawl through opposition groups. An enthusiastic agent, calling himself Alec Gordon, was assigned to penetrate it. Pretending to be a conscientious objector on the run, Gordon - whose real name was William Rickard - met and befriended Alice Wheeldon.
When he proposed a scheme to 'spring' a friend from an internment camp by poisoning the guard dogs, Alice agreed and asked her son-in-law, Alf Mason, a chemist, to supply the drugs. Mason sent her a fully-equipped 'poison kit', including almost every known lethal poison, in a tobacco tin. But it was intercepted in the post.
At this point, according to historians, Gordon inflated the 'poisoned dogs' plan into a conspiracy to kill Lloyd George. Alice, Hettie and Winnie were said to be preparing to assassinate the prime minister on Walton Heath, where he played golf, using an air- rifle pellet dipped in curare, the poison used on arrows by South American Indians.
The accusation aroused a storm of controversy and has gone down in socialist annals as a blatant example of state persecution. Dr Hiley said: 'The whole case against the Wheeldons was suspect from start to finish. It depended on the word of one man, Gordon, who was paid by results. The only corroboration came from Gordon's employers in MI5. In a sense it was a show trial. It demonstrated how far the government was prepared to go to preserve its position. There was a strong feeling in left-wing circles at the time that the Wheeldons were being made an example of.'
The trial marked a significant point in MI5's history. The unit that investigated Wheeldon, known as PMS2, was a highly secret organisation responsible for placing spies in munitions factories with the aim of identifying ringleaders of potential strikes.
In December 1916, a bitter feud was being fought between MI5 and the police Special Branch over responsibility for spying on industrial unrest. When Gordon telegraphed from Derby, 'Plot to murder Lloyd George and Arthur Henderson (the Labour leader) - come at once,' his superiors at MI5 saw an opportunity to show that their spy network was indispensable. It was the point when MI5 moved from its early role of combating German influence to the investigation of any group opposed to official policy.
After a three-day trial in March 1917, Alice, Winnie and Alf Mason were given long prison terms; Hettie was acquitted. However, there is evidence that even Lloyd George did not believe the accusations. Within two years he had personally arranged for all their releases.
Alice, weakened by a hunger strike, died in 1919, and Willie came out of hiding to lay a red flag over the coffin at her funeral. A few months later an amnesty was declared for conscientious objectors. Willie applied for his job back, but was refused because he had been to prison. He moved to Croydon to run a dairy. In November 1920, Hettie - who had married Arthur MacManus, first chairman of the Communist Party of Great Britain - died after giving birth to a stillborn child.
The following year Willie emigrated to Russia, apparently to start a new life. The Russian civil war had come to an end, Lenin was in power, and the New Economic Policy had just been introduced. Compared with his life in England, the prospects there must have looked bright.
Until last week, Dr Hiley was unaware that Wheeldon had died at the hands of Stalin's agents. No details have been given in Moscow to explain why Wheeldon was executed, or exactly when or where he met his death. But it was known that he took Russian citizenship and seemed to have planned to spend the rest of his life there.
'I was always under the impression that he died in a great typhus epidemic in Russia in the 1920s,' said Chloe Mason, a descendant, who lives in Australia. 'I am glad this has come out. This is a story we have been trying to uncover for years. All I know is that he was a good correspondent and wrote frequently from Russia for years. The letters got sadder and sadder.' Willie was last heard of in the central Russian city of Samara (now Kuybyshev) in 1928.
Home Office papers relating to the Wheeldon trial are still classified. Dr Hiley said: 'There were so many secrets surrounding the family. It is fitting that something should have been revealed about Willie's last days. He was an individualist. He probably refused to toe the line in Russia any more than he had in Britain.'