At 11.30 on the night of April 7, 1779, Martha Ray, the 35-year-old mistress of the Earl of Sandwich, was shot dead at point-blank range on the steps of Covent Garden Theatre. Her assailant was a young clergyman, James Hackman, who then tried to shoot himself, but suffered only a slight graze to the forehead. He was apprehended immediately, "beating himself about the head . . . crying 'o! kill me! . . . for God's sake kill me!' " Twelve days later, he was hanged for murder at Tyburn before a huge crowd that included James Boswell.

There was an enormous amount of press interest in the case: a clergyman murderer, a woman shot dead amid a crowd of fashionable theatre-goers, a high-profile government minister exposed. But the reports, while relishing every detail of this shocking murder, cast no blame. On the contrary, Hackman was praised for his decorum on the scaffold, and pitied for his crime. His last words, reported Boswell to Johnson and Mrs Thrale, were "Dear Dear Miss Ray."

Ray, meanwhile, was said to have been "irreproachable in her conduct" and "had every Accomplishment that could adorn a woman". She was no casual courtesan: she and Sandwich had been devoted companions for 16 years (his wife suffered from mental illness and had been made a ward of court) and they had five children. Her portrait, by Nathaniel Dance, hung in the Admiralty, where Sandwich was First Lord.

Even Sandwich, under pressure because of the disastrous progress of the war against America, was treated sympathetically. In the past he had been caricatured as a notorious rake and rumoured to have seduced Ray when she was 18 (and he was 42) after giving her spiked champagne. But now the St James's Chronicle asserted that in this affair the Earl "has shown a Tenderness which does the highest credit to his Heart".

Hackman and Ray could be dismissed as just another Georgian crime of passion. But, says John Brewer in his preface to this elegantly written study, "no story is innocent; all narratives involve plotting". His interest is not in the actual details of the case, but rather in what this story can tell us about the workings of history, or rather historiography. How have successive ages reinterpreted this scandal? And what can these alterations of view tell us about "history"?

At first, says Brewer, the reports on the case sought to emphasise that Hackman was destroyed not by his wickedness but by his overwhelming affection for Ray, by his "sensibility". In 1780 Herbert Croft, a clergyman friend of Dr Johnson, published Love and Madness: A Story Too True, which he claimed was a collection of letters between Hackman and Ray. In fact only two letters were genuine, the rest were the outpourings of Croft's fevered imagination. "You have made me all heart from top to bottom," writes the fictional, love-crazed Hackman.

Croft's interest in this story is puzzling: he was a scholar whose Life of Edward Young was included by Johnson in his Lives of the English Poets. Was he simply cashing in on what had been a sensational scandal? Did he genuinely believe that Hackman and Ray's story could arouse the kind of "sympathy" that Hume regarded as ennobling?

A generation later, Wordsworth is associated with the crime. He was a close friend of Basil Montagu, third child of Sandwich and Ray, who had been nine years old when his mother was shot. In the Lyrical Ballads, the poet links Martha Ray's name with a woman who mourns the death of her illegitimate child. Brewer argues that Ray has now been transformed, by this post-Revolutionary world, into the victim not so much of Hackman's bullet but of the inequalities and debauchery of Georgian society.

Brewer's previous book, The Pleasures of the Imagination, created a rich portrait of Enlightenment culture in England, a feat both of historical research and literary endeavour. In Sentimental Murder he is seeking to dissect not just a crime of passion but the nature of "history" itself, and to defend what he describes as the blurring of the lines between history and fiction, facts and the imagination.

Such questions are, of course, of great import as we crumple beneath the flood of "facts" provided by the World-Wide Web, and succumb to the fascination of "reality" television. But there's something missing from this book; an absence, perhaps, of Georgian sensibility. Hackman and Ray's story, though tragic, is too slight to bear the weight of such great arguments.

The jacket shows a voluptuous woman (no relation to Ray) languorously dangling a mask in one hand, as if resting between dances at a masquerade. It's an invitation; come on in and be titillated by a new kind of history. The scene inside is colourful, fashionably attired and fizzing with entertainment. But what are we left with when the party is over?

• Kate Chisholm's books include 'Fanny Burney: Her Life' (Vintage).