When he wrote a poem for his secretary and lover Betty Mackereth in 1976, Philip Larkin sent it with a note: “Flog it to Texas if it seems embarrassing.” The joke was self-indulgent: Larkin knew libraries and archives – such as the Harry Ransom Centre, in Texas – would hurl themselves off a proverbial cliff just to get his scraps. Even his shopping list could be lucrative, so long as he signed it.

The British Library in London currently has a veritable goldmine papering its walls. Its Harry Potter exhibition is an eclectic curation of old books, scrolls and ephemera that have some (occasionally tenuous) connection to JK Rowling’s world. And among the Chinese fortune-telling bones (circa 1000 BC) and garden gnomes (circa 1900) are Rowling’s drafts for some of the bestselling books of all time.

JK Rowling’s original handwritten draft of chapter 17 of The Philosopher’s Stone. Photograph: Nils Jorgensen/REX/Shutterstock

While some authors would baulk at showing anyone, let alone hundreds of thousands of museum visitors, their “process”, Rowling is entirely unafraid of sharing even her ropiest Potter ideas in public. She does so at talks, on Twitter and on a website, Pottermore, where she publishes all her unexplored, unfinished plots for a starry-eyed audience. Dumbledore is gay! Harry’s grandfather made hair products! Lupin and Tonks got married in a pub in Scotland! Even for a fan, it is easy to feel suspicious of this seemingly endless post-Potter expansion. There is no hidden significance or justifying quality in Rowling’s titbits that explains their publication. No, we now know Harry’s transfiguration teacher Professor McGonagall had two brothers and a husband who died because Rowling and her publishers believe our appetite for Potter is insatiable – and on that, they’re probably right. What luck then, that Rowling has always written with pen on paper and has produced such a treasure trove, and how lucky too that revealing her failed or abandoned ideas is not an embarrassment to her, even when cushioned by such success.

The British Library exhibition shows a lot of them: an early draft of The Philosopher’s Stone in which Voldemort is described as a snort-worthy “red-eyed dwarf”; a deleted part from The Chamber of Secrets, where the Weasleys’ flying car is rescued by mer-people after landing in the lake instead of the Whomping Willow; a clumsy scene from a Philosopher’s Stone draft, in which Hagrid pays a visit to Cornelius Fudge, the magical minister in the books and only an ordinary MP in the draft (“Mrs Fudge and I were thinking of moving to Portugal. We have a villa …”), who also has a colleague called Vernone Dursley, whose son is named Didsbury. There are countless tiny glimpses of characters that would never be: it’s hard not to wonder what Enid Pettigrew, Oakden Hernshaw and Mylor Silvanus, all named, then abandoned, would have been like.

Rowling’s scratched out, scrawled pages show the extensive tweaking she performed on her writing, from The Philosopher’s Stone to The Deathly Hallows. There are little annotations scattered everywhere (“[This way],” ends one page, with a backwards arrow, a helpful direction for its author). The short-term brain freezes are visible (“‘Hermione, let me down!’ Harry yelled”, is scrawled out on a page of The Deathly Hallows and replaced with just: “‘X’ yelled Harry”).

Immerse yourself ... Photograph: Nils Jorgensen/REX/Shutterstock

Perhaps the most interesting writing on the pages is not Rowling’s but that of her editors. Some of their notes read almost as chastisements of her imagination – such as one on a page from The Half-Blood Prince, where Harry notes that a potion his teacher has just shown him takes six months to make (“So Slughorn has some ready prepared for their first lesson, presumably!”), or the abandoned watery end for the Weasleys’ flying car (“I wondered whether the mer-people scene actually works?”). One particularly funny query is found on a draft of The Half-Blood Prince, where an editor circled a “dammit” dropped by 16-year-old Ron: “At this age, swearing would be so much stronger??” (Harry and company are not known for their effing and jeffing).

Cynics will view these manuscripts as the miserable dregs from an over-lauded cup of tea. They are actually hugely impressive – because, for all the notes and editor marks, the most amazing revelation is how sure Rowling seemed about her creation from the start. A handwritten draft of the Sorting Hat song has barely any changes, Harry’s class list is exact, and her hand-drawn map of the Hogwarts grounds, complete with a wonky giant squid bobbing in the lake, is the school we know.

But with so many proposed alternatives and unfinished ideas made public, both here and on Pottermore, it’s hard not to suspect that Rowling may end up like Nabokov, Kafka or a literary Tupac Shakur: either having her every note pored over posthumously for another book, or cursed into an artistic purgatory with awful output she never intended to release. This is not to suggest Rowling does a Salinger (burn her notebooks, retreat to live on a diet of raw food and I Love Lucy). Perhaps Terry Pratchett had the right idea: take a steamroller to the lot. Still, even his thoroughly squashed computer drive is now on display, in a museum in Salisbury.