We all get older, and so do our books. Two years ago, Philip Pullman met the challenge of returning to the world of His Dark Materials by going back in time. La Belle Sauvage, the first volume of his planned trilogy The Book of Dust, was a prequel, telling how, as a baby, Lyra Belacqua was saved from the deadly agents of the Magisterium, the authoritarian church that is always seeking to extend its powers. Her rescuer was the heroic but thoroughly human Malcolm, an 11-year-old living with his parents in a pub on the river outside Oxford. Now, in The Secret Commonwealth, the second volume of The Book of Dust, Pullman does something riskier: he jumps forward 20 years – a decade on from the memorably sad, satisfyingly inevitable ending of The Amber Spyglass – to give us the story of Lyra as a young adult.

Now she is a student in that familiar-yet-strange Oxford of Pullman’s alternative world. (This book stays in that world and never crosses to our own.) She has become very intellectual and a little solemn and has fallen out with her daemon, Pantalaimon. But she cannot retreat into her books, as she soon realises that she remains a person of interest to the Magisterium. The book’s gripping opening chapter moves between sinister machinations among leaders of the church in Geneva, and a clumsy murder in night-time Oxford. The murder victim, Lyra discovers, is a botanist – mystical botanical lore is at the heart of this tale. He had recently returned from a research trip to Central Asia where, we strongly suspect, we will eventually be led.

Everyone is older. Malcolm, whose help Lyra soon recruits, has grown into an eccentric young academic with a tendresse for Lyra, his former student, that is distinctly adult. Other characters from the earlier books return, a little time-worn, to assist our heroine. As she flees the deadly theocrats, there are plenty of the thrills you might recognise from His Dark Materials, yet this is a long way from that work. “Not suitable for younger readers,” warns the Waterstones website. There is graphic violence and an attempted gang rape. There is also some depiction of Lyra’s awakened sexuality, though Pullman makes her seek out the company of men to whom she is not attracted, so that she cannot be unfaithful to the absent Will, forever lost to his parallel world.

Pullman seems to be writing for those who read the HDM novels as children, but are children no longer. Lyra herself is naggingly conscious of what she has lost from the earlier books. Asked an awkward question by a suspicious stranger, she fails to produce the fearless lies she would once have managed, and thinks to herself that “now she just lacked inventiveness, or energy, or chutzpah”. Pantalaimon tells her that she has become “cautious … anxious … pessimistic”. The two of them become literally as well as psychologically separated; one plotline follows Lyra’s quest to recover her daemon, without whom she appears to others as “an appalling and uncanny figure” – and also, we discover, newly vulnerable.

Philip Pullman. Photograph: Murdo Macleod/The Guardian

She has had her head turned by seductive books. Her daemon goes on a long journey to Wittenberg (the city of Martin Luther, where Hamlet went to university) to accuse the stern intellectual, Gottfried Brande, of stealing Lyra’s imagination from her. Brande has published a huge novel written in a prose purged of all figurative language, which proposes that daemons are illusions: it has become a vogue throughout Europe. Meanwhile Lyra journeys towards the east, while Malcolm separately tracks her. There is always plenty of dizzying travel in Pullman’s fiction, here more breathless than ever. Lyra meets an alchemist in Prague, witnesses an assassination in Constantinople, narrowly avoids being killed in Smyrna.

A paranoid gent at a central European railway station or a wizened old lady in a Levantine port only has to mention a distant destination for Lyra or Malcolm to hurtle off towards it. We know that the answers to the book’s various teasing puzzles must lie in that fabled botanical research station (but perhaps beyond the bounds of this particular volume). Pullman’s narrative method is to divide our attentions not only between Lyra, Malcolm and Pan, but also between them and the leading operatives of the Magisterium, scheming and debating about how to perpetuate their chilly faith. We keep going back to the Maison Juste in Geneva, the world centre for “the examination of heresy and heretics”. Here we get a good deal of ecclesiastical power politics, with the deliciously Machiavellian Marcel Delamere eliminating rivals and concentrating power in his own hands. The satire of religious flummery is even more explicit and withering than in the original trilogy. Indeed, Pullman is more tempted to draw parallels with our world’s discontents than he has ever been. Our own refugee crises and confrontations with Islamic fundamentalism (here “the brotherhood of the holy purpose”) have their ready analogies in his fictional universe. Lyra is pitted against not only the agents of theocracy but also a ruthless multinational chemical company.

His main target here, however, is as much intolerant rationality as intolerant theism – the life-denying Reason that William Blake, his literary guide, deplored and mocked. The Magisterium has recruited a clever nihilistic philosopher, Simon Talbot. He is their “useful idiot”. Lyra so relishes intellectual dispute, “searching out the weaknesses in someone else’s arguments, and cracking them open with a flourish”, that she has fallen under his sway. Blake would certainly have concurred with Pullman’s satire on showily rationalistic philosophy, a scepticism so complete that it deadens the soul.

Imagination, the mysterious power celebrated by the Romantic poets, is the holy spirit of this book

Thus, the importance of “the secret commonwealth”, which is the world beyond rationality. Lyra begins to realise that it is what she has left behind in her childhood (and in the original His Dark Materials trilogy). “It was quite invisible to everyday vision … it was seen by the imagination, whatever that was, and not by logic.” As one of the many advisers she meets tells her, its affairs sometimes “leak through into the visible world”. Lyra must find her daemon again to put herself back in touch with it, to rediscover Blakean innocence.

Pullman has successfully turned his heroine into an adult by making her remember herself as a child, which also means remembering the earlier books that we all loved. But there is a downside. Previously, Lyra’s experiences and Pullman’s ideas were separate. As a child, she did not know what her story meant. Now she can ruminate in tune with the author’s purposes. “Has reason ever created a poem, or a symphony, or a painting? If rationality can’t see things like the secret commonwealth, it’s because rationality’s vision is limited … We need to imagine as well as measure …” This is Lyra thinking, but it is also rather too clearly Pullman speaking to us.

Imagination, the mysterious power celebrated by the Romantic poets, is the holy spirit of this book. It opens with a contrarian epigraph from Blake: “Everything possible to be believ’d is an image of the truth.” This declaration sounds permissive (you can believe whatever you like) but is in fact stern (you should listen harder to the logic of your instinctual beliefs). It is the law of fiction that Pullman obeys. He has created a fantasy world, made yet more satisfying in this new volume and pursued with his own special rigour and stylistic elegance. This is a book for getting older with.

• The Secret Commonwealth is published by Penguin/David Fickling (£20). To order a copy go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £15, online orders only. Phone orders min p&p of £1.99.