Michael Cunningham's novel has an epigraph from Virginia Woolf's diary entry for 30 August 1923, when she was at work on her fourth novel, Mrs Dalloway. This work in progress still has her provisional title, "The Hours", which Cunningham has duly taken for his own book. It is the first sign of his activity of imitation. In the prologue of The Hours we are asked to imagine, as if from her point of view, the day of Virginia Woolf's suicide. But this is not a fictionalisation of her life and death; it is an imitation  a reworking  of her novel, Mrs Dalloway.

The prologue is followed by a second section, titled "Mrs Dalloway", in which a 52-year-old woman called Clarissa Vaughan goes shopping for flowers in New York on a June morning at "the end of the twentieth century". Woolf's novel begins with a woman called Clarissa Dalloway leaving her London house on a June morning to buy flowers for a party. Has Cunningham's character not noticed, you feel like asking, that she is acting out the opening of a famous novel? She certainly knows Woolf's fiction. Her friend Richard has even dubbed her "Mrs Dalloway", scorning her own itch to be likened to a heroine from Tolstoy or Henry James. Her "existing first name", he suggests, is "a sign too obvious to ignore". And anyway, she is no tragic protagonist, but a woman, like Woolf's Clarissa Dalloway, "destined to charm, to prosper".

We follow Clarissa Vaughan, walking through the streets of New York, as Woolf's narrative followed Clarissa Dalloway. Woolf's protagonist passes a man called Scrope Purvis, and we suddenly catch his thoughts, as if they were some briefly audible skein of sound. ("a touch of the bird about her, of the jay, blue-green, light, vivacious, though she was over fifty"). In The Hours, Clarissa is spotted at the corner of Eighth Street and Fifth Avenue by Willie Bass, who more bluntly considers her "certain sexiness" ("She must have been spectacular twenty-five years ago") and then, as the light changes, walks on, unnoticed by her.

There are little jokes for the reader who knows the original. Woolf's protagonist is at the florist's when she is startled by a car backfiring ("oh! A pistol shot in the street outside!"). In the back of the car passers-by glimpse "a face of the greatest importance". "Was it the Prince of Wales's, the Queen's, the Prime Minister's?" (The prime minister will later arrive as a guest at the party for which Clarissa Dalloway is preparing.) Cunningham's character is distracted from her purchase in a flower shop by a loud noise from the street, where filming is taking place, and the sudden appearance from a trailer of a well know profile "(Meryl Streep? Vanessa Redgrave?)".

Yet the novel has two other narrative threads. In the next section "It is a suburb of London. It is 1923", and Virginia Woolf is thinking about how she might begin the novel that she is supposed to be writing. At the end of it she writes the first sentence of that novel. There it is. "Mrs Dalloway said she would buy the flowers herself." And then that sentence, repeated, opens the next section of the novel (titled "Mrs Brown"), as Laura Brown, a housewife in Los Angeles in 1949, reads Mrs Dalloway to herself. The narrative focusing on her includes long passages from Woolf's novel, laid out on the page in italic font.

Cunningham gives you every chance to hear his echoes of Woolf's style: the whimsical similes, the rueful parentheses, the luminous circumstantial detail. And the narrative method is a homage to Woolf's novel. Each section imitates Mrs Dalloway by being restricted to the events of a single day, and follows the stream of one consciousness, only to leave it, for a sentence or a paragraph, for another. Though each section of Cunningham's novel concentrates on one of its three leading characters, the narrative can always shift between different consciousnesses. As Virginia Woolf talks to her husband Leonard, we suddenly enter his mind too ("She may be the most intelligent woman in England, he thinks"). As Laura Brown makes a cake with her son, we inhabit his mind as well as hers ("He understands that he's expected to dump the flour into the bowl but it seems possible that he's misunderstood the directions, and will ruin everything").

The Clarissa Vaughan sections go further: they parallel the episodes and the characters of Woolf's original. Septimus Warren Smith, the shell-shock victim in Woolf's story who hears the birds in Regent's Park speaking in Greek, becomes Clarissa's one-time lover Richard, dying from Aids, who is haunted by spirits singing "in a foreign language. I believe it may have been Greek". If you have read Mrs Dalloway, you will guess how Richard's story might end. Yet plot is incidental.

Imitation is fitting because Woolf's original novel was trying to do justice to the sharpness of new experience, even as it detonates old memories, and this endeavour is always worth trying afresh.

John Mullan is professor of English at University College London. Join him and Michael Cunningham for a discussion on Tuesday 5 July at 7pm, Hall Two, Kings Place, 90 York Way, London N1. Tickets £8, from www.kingsplace.co.uk (020 7520 1490).