The words "bible" and "orgy" don't often appear in the same sentence, but the 400th anniversary of the publication of the King James Bible has prompted an orgy of celebrations and meditations, ranging from staged and sponsored readings of its text to erudite essays and the creation (in Peterborough) of a giant model out of approximately 3,000 shoe boxes.

Melvyn Bragg's contribution to this commemorative feast is a populist account of the impact of what frequently gets called the Authorised Version  a name that caught on only in the 19th century. His is a book not about the making of the King James Bible, which is dealt with briskly, but about its effects: its role in the movement to abolish slavery and its place in the charitable endeavours of the Victorian social reformer Octavia Hill, its worth as literature and its capacity for invigorating writers as different as John Milton and DH Lawrence.

If you want a meticulous, scholarly treatment of its cultural resonance, you would do better with The King James Bible After 400 Years, a volume of essays edited by Hannibal Hamlin and Norman Jones. Gordon Campbell's Bible: The Story of the King James Version is stronger on its American afterlives. In Begat: The King James Bible & the English Language, David Crystal has probed the question of the work's true influence on common idiom  with surprising results.

But Bragg's tribute is of value because he has an aptitude for storytelling. He is breezily readable where other studies can feel dense and recondite. His turn of phrase is dramatic: describing the King James Bible's popularity, he writes that "since 1611 it has flooded over the world". Later, he says it "let loose a deluge of knowledge unlike anything that had happened before in human history". Saluting the efforts of the 54 men who translated the Hebrew of the Old Testament, and the Greek of the New Testament, he avers that "because of them we speak out of that book still, every day of our lives".

Bragg's prose reverberates with scriptural certainty. He can become vociferously insistent, as when dealing with Richard Dawkins  who "preys on anecdotal evidence", "worships statistics", "swoops into neuroscience", and who is characterised for no fewer than 16 pages in terms befitting an Old Testament plague.

Yet mostly this is an affectionate book, coloured by Bragg's personal response to a volume he first encountered when he was six. In The Adventure of English (2003) he remarked of his Cumbrian childhood that "the King James Bible gave us not only cadences and rhythms but metaphors and references". Here he recalls how its stories and admonitions "provided both meat for argument and grist for guilt".

Bragg's central claim is that the King James Bible has been a catalyst for "positive achievement", spurring political radicalism and epochal social changes. He identifies it as a wellspring of democracy and the source of Mary Wollstonecraft's convictions about the importance of women's education. He makes a case for its influence on Thomas Paine and William Wilberforce, on the moderate socialism of James Keir Hardie and the non-violent activism of Martin Luther King. He also touches on the odious ways it has been deployed, such as in justifying homophobia, though he could have reported these at greater length.

Occasionally the argument seems stretched. Yes, many of the social and political changes Bragg relates were accomplished by people who were intimate with the King James Bible; however, this is not to say that the King James Bible was their chief inspiration. And when he discusses its 20th-century literary influence, Bragg's largely fluent narrative begins to resemble a list, in which he makes some glib transitions  "Like TS Eliot, Toni Morrison won the Nobel Prize for literature".

Often in this wide-ranging book, Bragg strikes a triumphalist note; but he finally concedes that his project is nostalgic. He admires what he calls the "gallantry" of 21st-century churchgoers; in the face of rampant secularism, they "hang on". In the end "the whole idea  God, Genesis, Christ, Resurrection  is a moving metaphor". Yet while The Book of Books may conclude elegiacally, it demonstrates energetically that this metaphor, as realised by a committee of Jacobean scholars, has exerted an astonishing magnetism.