“Tony Blair was once a Trot!” Variations of this headline appear on most news sites today. In an interview with historian Peter Hennessy on Radio 4, Blair has spoken of how Isaac Deutscher's masterful biography of Trotsky briefly drew him to revolutionary socialism.

“Here’s this guy Trotsky, who was so inspired by all of this that he went out to create a Russian revolution and changed the world,” Blair recalled. “I think it’s a very odd thing – just literally it was like a light going on.” Pressed on whether he was “briefly a Trot”, Blair replied: “In that sense I was.”

The story isn't strictly new. Blair has previously cited Deutscher's Trotsky trilogy (The Prophet Armed, The Prophet Unarmed, The Prophet Outcast) as one of his favourite works. In a 1982 letter to Michael Foot, unearthed in 2006, Blair wrote: "Like many middle class people I came to Socialism through Marxism (to be more specific through Deutscher's biography of Trotsky)". But the story is perhaps eye-catching enough to be worth telling twice.

Yet Blair is actually rare among New Labour figures in having only, as he puts it, "toyed with Marxism". Peter Mandelson, one of the project's architects, joined the Young Communist League, rather than Labour, in protest at Harold Wilson's support for the Vietnam war. The future business secretary attended a youth conference in Cuba (a visit recorded by the British intelligence services) and sold the Morning Star outside Kilburn tube station.

John Reid, another future Labour cabinet minister, was also a member of the Soviet-aligned Communist Party of Great Britain. "He told us he was a Leninist and Stalinist," Jim White, a fellow party member later recalled. "Although I was suspicious about his transition, we couldn't tell if he was acting. We let him join."

Others, dismayed by the Soviet Union's degeneration, were drawn to Trotskyism. Future chancellor Alistair Darling was a supporter of the International Marxist Group, the sect to which soixante huitard Tariq Ali belonged. "When I first met him [Darling] 35 years ago," George Galloway once recalled, "Darling was pressing Trotskyite tracts on bewildered railwaymen at Waverley Station in Edinburgh. He was a supporter of the International Marxist Group, whose publication was entitled the Black Dwarf. Later, in preparation for his current role he became the treasurer of what was always termed the rebel Lothian Regional Council."

Stephen Byers, the future transport secretary and Blairite-ultra, was a supporter of Militant, the entryist group later expelled from Labour by Neil Kinnock. Alan Milburn, who served as health secretary under Blair, was another youthful Trotskyist, running Marxist bookshop Days of Hope (known to locals as "Haze of Dope").

Though all renounced their revolutionary politics, some detected remnants in New Labour's fondness for "command and control" (reminiscent of Leninist democratic centralism). And while Labour has never been a Marxist party, Marxism has long been a strain within it. Tony Benn, a rare example of a politician who moved leftwards with age, regularly cited the lessons of Das Kapital and the Communist Manifesto. Asked to name the "most significant" influences on his thought in 2006, John McDonnell (who was then standing for the Labour leadership) replied: "The fundamental Marxist writers of Marx, Lenin and Trotsky, basically."

Blair's youthful Trotskyism makes his professed bemusement at Jeremy Corbyn's rise all the more surprising ("I really mean it when I say I’m not sure I fully understand politics right now," he remarked). Just as the former PM was drawn to radicalism, so Labour's young (and old) members were inspired by Corbyn's unabashed socialism. Rather than lamenting the Islington MP's rise, Blair and his ideological successors would do better to learn from it.