It is a truth universally acknowledged that if ever a novelist deserved a three-hour documentary deploying all the experts, all the excerpts from book and screen, all the re-enactments, all the life, all the literature, every bell and whistle, it is Jane Austen in the year 2025, the 250th anniversary of her birth.

So, here it is – Jane Austen: Rise of a Genius. It’s a title that doesn’t mess around and neither does the programme, a prestigiously-bound triple-decker narrated by Juliet Stevenson that takes us through Austen’s birth, background, personal life, creative imagination, publishing history, private and professional setbacks and successes, with all the care and close attention a fan could wish for.

A host of informative Janeites gather for the event, among them her biographer Dr Paula Byrne; academics Dr Priya Atwal, Dr Louise Curran and Dr Paddy Bullard; writers Bee Rowlatt, Candice Carty-Williams, Helen Fielding, Colm Tóibín and Kate Atkinson; “Renaissance man” Sam West (don’t write in – that’s metaphorical; I know we’re Georgianning); actors Tom Bennett, Charity Wakefield, Greg Wise and many more. The mood is impassioned and enthusiastic without being emetic – suffused with love of the work, and mapping the contours of the specific genius without anyone getting un-Janeishly carried away. You feel she would approve.

Off we go, then, back to the genteelly impoverished childhood as one of the eight children of a hardworking rector father. He gave his daughter two great and rare gifts for the time: his unwavering support of her gifts from the first days they made themselves known, and unfettered access to his 500-volume library, which included many examples of the novelty form that was then the novel. One of her earliest writings is the story of The Beautiful Cassandra, whose heroine – named after her beloved sister – is an adventurous young miss who storms round London punching pastry chefs. It will have you immediately online locating the nearest copy of the juvenilia you can find.

On through Lady Susan, the bereavements, the broken engagements, first publication at the age of 35, the big six books, the growing confidence and success, the patronage of the Prince Regent (she didn’t like him or the excessive age he created but he was the “influencer” of his day so she wisely accepted it), battles with publishers, the punishing illness through which she wrote the end of Persuasion and the beginning of Sanditon, and her eventual untimely death at the age of 41. She was, they say, at the peak of her powers – but how do we know? She may only just have begun the ascent. “The sun of my life, the gilder of every pleasure, the soother of every sorrow” as Cassandra wrote of her sister, who was buried in Winchester Cathedral with four people in attendance and a headstone that did not mention her career. Nor, feted though she was, did her name appear on any of her novels during her lifetime.

But, strewn with a generous hand along the chronology are rarer, deeper acknowledgments of Austen’s accomplishments and at least as much discussion of the less-adapted, more difficult novels. One such, certainly, is Mansfield Park, with its undertow of criticism of the slave trade and the people growing fat on the profits of human suffering, which went resolutely unreviewed by the press when it was published and unmentioned by Sir Walter Scott in his otherwise acutely perceptive 1815 appraisal of her work. Another is the melancholic final (completed) work Persuasion.

We are invited to marvel at her invention of what has come to be known as free indirect style, whereby the voices of characters shift almost imperceptibly into the voice of the narrator and vice versa, so that you discern their thoughts and commentary on them at the same time (and, as Tóibín puts it, “becomes a drama between the reader and the page”). Likewise, her concept of the unreliable narrator, and the beauty and economy of her language, whether in famous opening lines, agonising marriage proposals or perfect, peerless declarations of enduring love. “I am half agony, half hope” (Persuasion) …

It is a documentary that discharges its duty well and fully – not least in inspiring most of the audience, I am sure, to head straight back to the books and glory in them anew.

• Jane Austen: Rise of a Genius aired on BBC Two and is on iPlayer now.