On the afternoon of 12 September 2015, Jeremy Corbyn celebrated his remarkable victory in the protracted, summer-long Labour leadership contest by joining friends and supporters in a pub for a rendition of the socialist anthem “The Red Flag”. A few weeks later, as the Leader of Her Majesty’s Opposition, Corbyn embarrassed himself and his party by failing to sing the National Anthem at a Battle of Britain memorial service at St Paul’s Cathedral.

The juxtaposition of these two events would have told the curious onlooker all he needed to know about the man preaching “the new politics” and aspiring to be our next Labour prime minister. For Corbyn is what George Orwell called, in The Road to Wigan Pier, a “crank”. “One sometimes gets the impression,” he wrote, “that the mere words ‘Socialism’ and ‘Communism’ draw towards them with magnetic force every fruit-juice drinker, nudist, sandal-wearer, sex-maniac, Quaker, ‘Nature Cure’ quack, pacifist, and feminist in England.” They flock towards “the smell of ‘progress’ like bluebottles to a dead cat”, Orwell said.

Until he was elected Labour leader, Corbyn’s Westminster career had been a study in irrelevance, as Rosa Prince explains in Comrade Corbyn, her accomplished new book. He was first elected to the Commons as an MP as long ago as 1983, the same year as Tony Blair. But, before becoming leader of the opposition, he had never served as a minister or shadow minister and had run nothing apart from his constituency office. A serial rebel, he spent much of his time in parliament defying the party whip as he indulged his ideological obsessions.

As Rosa Prince shows, over the long years of campaigning, Corbyn built up a vast network of contacts on the far left and among Trotskyite sects, which proved very useful after Labour changed the rules by which it elects a leader, allowing anyone who paid £3 to register as a supporter and vote. There are few radical causes, it seems, that Corbyn has not supported, from the Troops Out Movement to Stop the War and CND. At times, he has been on the right side of history, such as when campaigning against apartheid South Africa or the American-led invasion of Iraq. At other times, his behaviour has been reprehensible; in 1984 he invited leading members of Sinn Fein/IRA to Westminster shortly after the attempt to murder Margaret Thatcher and her cabinet at their hotel in Brighton.

Corbyn might be mild-mannered but he has repeatedly demonstrated that he is an extremist. His opinions are seldom expressed stridently, which for some is part of his appeal. But he is an extremist all the same and his refusal to compromise and his hard ideological commitments are worn like badges of honour. That such a man should be leader of the opposition is further proof, if any were needed after the dismal years of Ed Miliband’s leadership, of how enfeebled the party of Clement Attlee and Tony Blair has become and of how disenchanted so many have grown with the whole Westminster jamboree.

Jeremy Corbyn is a difficult subject for a biographer. Where does one turn, for instance, for a full exposition of his political thought? He has written nothing of value; there are no books or essays. There are no published diaries of the kind kept over many years by his mentor Tony Benn and which Prince mines for references to Corbyn. Instead, one must turn to the scrappy columns he published in the communist Morning Star newspaper and the speeches he delivered during the Labour leadership contest, which were inevitably the work of many hands and essentially platitudinous.

If there are notebooks and letters, Prince has not had access to them. She has interviewed many of those who know Corbyn well, such as the writer Tariq Ali, and many of his fellow MPs, but she does not succeed in giving us a rounded sense of his inner life and motivation. Complexity is absent from this portrait, perhaps because Corbyn is ultimately a simple-minded man.

The son of a “brilliant” electrical engineer, he grew up as one of four sons in an affluent middle-class family in rural Shropshire. Home was a seven-bedroom manor house that had once been a hotel, and he was educated at a fee-charging prep school and the academically selective Adams’ Grammar School, from where he emerged with two E-grade A Levels. This did not qualify him for university, and so he went off to work in Jamaica under the Voluntary Service Overseas scheme.

Corbyn’s hard-left, anti-American, anti-imperialist worldview has been unchanged since his late teens. In effect, Prince suggests, since he returned from his two years in Jamaica Corbyn has been suspended in a kind of perpetual adolescence, locked in a state of permanent rebellion. “I personally have always seen Jeremy as a Peter Pan figure, just not a grown-up,” one unnamed friend tells the author.

This seems to me an essential insight. When I interviewed Corbyn last summer he came across as part holy innocent, like Dostoevsky’s Prince Myshkin, and part Chauncey Gardener, as portrayed by Peter Sellers in Being There, a man whose utterances about peace and justice are so self-evidently banal that they somehow acquire a kind of mystical significance. It’s all good fun for those of us who write about him but a sad state of affairs for the Labour Party.

One of Corbyn’s long-time allies is Ken Livingstone, whom the conservative journalist Charles Moore has correctly called the “only truly successful left-wing British politician of modern times”. Unlike the Labour leader, Livingstone has actually occupied positions of considerable power, as a head of the old Greater London Council and mayor of London, and has done much more than agitate from the margins.

Being Red is subtitled “Politics for the Future” but it is nothing of the kind. It offers little more than a restatement of familiar prejudices and Livingstone’s brand of cheeky-chappie Left-populism. He scourges Tories, Blair (he “gutted the Labour Party” and believed “the neoliberal lie”), the right-wing press and multinational corporations.

On foreign affairs, Livingstone is a Manichaean. For him, the United States and its nefarious ally Saudi Arabia are responsible for most of the world’s ills since the end of the Second World War. He has no sense of the tragic dilemmas and necessary compromises of statecraft – or at least prefers to close his mind to them. “Man’s capacity for justice makes democracy possible; but man’s inclination to injustice makes democracy necessary,” wrote the American philosopher Reinhold Niebuhr, a favourite of Barack Obama’s. Such subtleties are beyond Livingstone.

Yet Livingstone is still capable of pragmatic good sense, as he demonstrated when as mayor he introduced the congestion charge, oversaw the modernization of the Tube and helped bring the Olympics to London. He thinks big and believes in long-term planning and state investment in grand infrastructure projects such as Crossrail and HSE2.

Being Red is a curious hybrid that comprises soft interviews with Livingstone (typical question: “You are an incredibly good media performer?”) and pieces by him (one hesitates to call them “essays”). I enjoyed the former – during which you hear the authentic Livingstone voice: scabrous, snarky, amused – but not the latter. He is no writer and one quickly tires of his absolutism without ever quite being able to dismiss him as one of Orwell’s “dreary tribe” of cranks.