"Writing a novel," says 21-year-old Samantha Shannon, "is like knocking on a door that will never open. You are so desperate to get in, you will say or do anything. You feel: please take my novel." She knows about being rejected. Her first attempt at a novel, she explains, was a failure – no matter what she tried, she could not find it a good home. But she also knows about persistence. We are sitting outside on an idyllic summer day, at the end of Shannon's mother's garden, not far from Rickmansworth. A canal ripples at our feet, ducks are trying to join in the conversation. It could not be a less appropriate setting – a sunny parallel universe – in which to consider Shannon's phenomenal achievement in having her dark, embattled, highly wrought fantasy, The Bone Season, taken on by Bloomsbury. Projected as a seven-book series, it has been bought for a six-figure sum (for the first three books). Rights have been sold on both sides of the Atlantic and in 20 countries (India is said to be especially keen). Film rights have also been fought over, but Shannon has not had her head turned by Hollywood, opting for Imaginarium, Andy Serkis and Jonathan Cavendish's independent film company.

Independence defines Shannon nicely. Hype about "the new JK Rowling" is in the air, but her writing is in no way like JKR's – she is her own woman. She has just come down from Oxford, where she was reading English (she managed a 2:1). Her system there was: study by day and, after dinner, write (good coffee essential). Now she is on vacation – it must feel unreal. She admits the past months and having the book accepted have been "overwhelming". I'd assumed she would come across as super-confident but, although highly articulate, she is a disarming combination of poise and shyness. Tall, pale and pretty, she is, at first, visibly nervous, which makes her look even younger than she is.

I ring Bloomsbury's editor-in-chief, Alexandra Pringle, to pin down what captured her about The Bone Season and she confesses it took her by surprise: she is not ordinarily a fantasy fiction fan. Shannon got past her defences – partly because the first book is plaited into reality (some of it is set in Seven Dials, Covent Garden). "It combines a 19th-century Dickensian quality with the futuristic. It is about glory and beauty – she has a fairy-tale imagination that has links with Beauty and the Beast but also with Angela Carter. Her work reminds me of all three Brontës sitting round a table creating an imaginary world."

The novel opens in 2059, in a London governed by a security force called Scion. Here, the 19-year-old Irish heroine, Paige Mahoney, is a clairvoyant, dreamwalker and informer – her special talent breaking and entering people's minds. But disaster strikes: she is mugged, drugged and taken to Oxford… The Oxford connection alone means that comparisons with Philip Pullman's Northern Lights trilogy are bound to occur. Pringle alludes to an exhibition at the Bodleian this summer entitled Magical Books, which looks at Oxford-inspired authors including Pullman and Tolkien. She sees Shannon – the fact that she is a woman an additional satisfaction – as the newest link in that magical chain.

Yet Shannon (although a JK Rowling devotee) has never read Pullman: "I thought it best to keep his world out of my head." Her version needed to be discrete – her Oxford is a penal colony, a contaminated place. It is run by "Rephaites" – unearthly creatures, the most charismatic of whom is the Warden, a sinister yet alluring donnish fellow with honey-coloured skin, amber eyes and scars aplenty. He lives in Magdalen Tower, where he keeps Paige captive – as if in some inescapable tutorial. You need the glossary at the back to keep up with the archaic vocabulary: Querents (persons seeking knowledge of the ether), meatspace (the Earth), flux (drug causing pain and disorientation in clairvoyants)...

"People question what I thought of Oxford. Students used to talk about the 'Oxford bubble' because the place can make you feel cut off from the rest of the world. I would forget there were places like London that were not centred round libraries and essays. It is a strange world, Oxford – quite claustrophobic. I was often glad I was only there for eight weeks at a time."

She grew up in Ruislip and went to Bishop Ramsay, the local state school. Her stepfather, Mike, is a plumber and her mother, Amanda – understandably brimming with pride – works as a health and safety manager for a glass processing company. Her father is a retired policeman and she has four half-siblings. Amanda (waiting on us hand and foot with cool drinks) tells me what a bookworm Samantha (never "Sam") always was. She still is, wishes she could slow down (currently racing through Koushun Takami's Battle Royale). And she fills me in on her education taking another tack – her path to becoming published.

Writing her first novel, Aurora, was like "a drug I couldn't stop taking". It was an "addictive chore". It hooked her to the extent she would get "cross" if anyone tried to tear her away: "I was writing so much I made myself ill. I had panda eyes. I was tired all the time." Her mother worried about her. At 19, Samantha self-deprecatingly records in her blog that she was still wearing braces and felt something of a social recluse. She was conscientious bordering on fantatical about the novel, even buying a book on how to self-edit (Self-Editing for Fiction Writers) and polishing her prose to death. When she sent the novel to agents, the rejections came back thick and fast – some of which her mother put in the bin unread.

Her father knew someone in touch with literary agent David Godwin and, after an email exchange, he agreed to look at her manuscript. He was "kind" about it but also turned the book down. Yet it was this connection that would not long afterwards lead to Shannon doing a two-week summer internship with his agency (in Seven Dials, Covent Garden), which was to prove illuminating about "how the industry works".

"I was on slush-pile duty, going through manuscripts, and began to see why they got rejected. People were writing these dreadfully impassioned letters – like the ones I had been sending. I'd feel terrible when their work didn't grab me. I would think: this is what must have happened with mine, the voice just didn't resonate." She marvelled at some of the unlikely manuscripts, remembering a particularly lengthy novel about Welsh farming.

By September 2010, she had resolved to give up on Aurora. "Then, early in 2011, at Oxford, I got this idea of writing a new novel, a dystopia mixed with the supernatural." From the start, the writing felt different – no longer an addiction, a healthier immersion (she was sleeping eight-hour nights). But it wasn't until February 2012, when she showed the opening chapter to novelist Ali Smith (who was also Weidenfeld visiting professor of European comparative literature at Oxford) that she got an inkling that the new book might be everything the first wasn't: "I went in shaking. I thought if she says this is rubbish, I will have to give up. But she sat down and just looked at me and said, 'Samantha, this is stunning.'" Smith suggested she might try an agent – and her own agent turned out to be… David Godwin.

Where was she when he told her Bloomsbury had accepted it? "I was in my room at uni. I remember sitting on my bed, staring at my computer and thinking, My God." She had once seen Alexandra Pringle at a book launch and thought, "What an incredibly glamorous woman…" and at the same time told herself categorically: "She will never publish my work." Pringle herself, when pressed, recalls a tall, thin, wordlessly shy young woman at the same party. She had forgotten Shannon until the day she met her again after signing her up.

The Bone Season has obvious crossover potential but is on Bloomsbury's adult list and Samantha is glad because "it means I am free to explore darker themes if I want to in later books". I ask about the violence in her writing – the sense that Paige is constantly in mortal peril, the restless suffering, the non-stop turmoil. "I do have a slightly overactive imagination I suppose," she laughs. She sees herself as "living vicariously" through Paige – somewhere between that and being her heroine's protector.

And so I tell her what I have been putting off until now – in case she takes it the wrong way – the oddest of tributes to the power of her fiction. A couple of nights before meeting her, I woke myself up with a scream. I thought I was dying by peculiar means: mobbed by the iridescent wings of butterflies. I was amazed by the inventiveness of my subconscious before recognising, almost in the same instant, that the nightmare's real author was Samantha Shannon. "I researched what a butterfly's vision is like. They see everything in ultraviolet, which is amazing." She adds that it was great "fun" to "design a butterfly's dreamscape". Her own inspiration, she adds, was the 14th-century Middle English poem Pearl. She also reveals that the entire book would never have materialised without Margaret Atwood's The Handmaid's Tale. "This was my trigger for wanting to write a dystopian novel… If I had to pick out one book that changed me, it was definitely that one. It gave me my feminist awakening as well."

She doesn't believe in the supernatural, in auras or clairvoyance. She is not much of a dreamer – at least not by night. She has a steady regard for the past and describes, in her blog, her love of music (from Chopin to the Ink Spots), gramophones and silent films – the list is charmingly dated, sedate even. And the pet she mentions, a male tortoise intriguingly named Lily-Beth, is no racer either. But she does tell me that she sees writing itself as a "kind of clairvoyance".

Without a soothsayer at hand, it is impossible to be sure how The Bone Season will fare. But she tells me she is already hard at work on the sequel: "For me, it is not a break to not write. Last summer, I wrote 500,000 words then decided I hated them and deleted them. Now, I am back to chapter four and glad I did it. It is much stronger now." Whatever the future holds, there is no doubt that Samantha is the real thing, her own sternest critic and a born storyteller: "I am never not thinking about stories. The Bone Season is 90% of my brain – 10% is interacting with the rest of the world."