The London Train is another Tessa Hadley novel about family relationships, though in this case neither a generational saga (Everything Will Be Alright) nor a tight domestic drama (The Master Bedroom). Here the protagonists are in motion, as the title suggests, their individuality more important to them than their sense of place, or responsibility, at either end of the line.

In the novel's first part, we follow Paul, a writer who lives in Wales and is well into his second marriage, though still picking up the pieces from his first. In the second, shorter and more gripping part, we follow Cora, wife of a senior civil servant who has fled back to her hometown of Cardiff following the failure of her marriage, in which the same Paul played no small part. This folding structure suggests a symmetry that the novel eschews: it is not clear, for example, how the relationship between Paul and Cora affects, if at all, Paul's story of searching for his adult daughter who has gone missing. But I would count this asymmetry among the novel's more mature virtues, which include absolute lack of predictability and scrupulous sincerity.

Both Cora and Paul inhabit the world of people who work for charities, read the Guardian and reside in white living rooms with exposed floorboards. Hadley reflects this world plainly and precisely, with its tension of fluctuating proximity to those who are the subjects of xenophobic Daily Mail headlines. She pinpoints the ambivalence of Paul, the British liberal, reacting to Marek (a Polish entrepreneur camping out in a council flat and doing dubious import/export deals), when Marek speaks in tabloid terms against the asylum system, but in a way that is beguiling "in the stream of his good nature and boundless energy".

At times Hadley's observational precision works like cinematic slow-motion, with patches of light travelling across people's rooms and bodies at important moments, as if referencing the lights of the passing train that flash across the heroine's tortured face at the end of Brief Encounter. Yet, even at its best, these are the metaphors for Hadley's writing skill  illumination and reflection  when what many of us crave from novels is something closer to refraction: the familiar and present day, perhaps, but not exactly as we know it. Maybe there are readers who do take unalloyed pleasure in self-recognition, but I suspect that most would share enough of these characters' individualistic ambitions to dislike feeling "typified", and it is surely one symptom of the liberal guilt and angst Hadley so accurately describes not to enjoy viewing one's own mirror image, even under the most sympathetic lighting.

As if with a chip on her shoulder about those who might say she writes middle-brow "women's fiction", Hadley has her characters discussing how such books can be "better than much so-called literary fiction, more true to life". But this, as the author herself obviously knows, misses the point. Masters of literary refraction, like Amis or Franzen, are less "true to life" and yet more so. Here the familiar remains just that, even though Hadley's imagery is unfailingly original in its detail, never cliched or mundane. Nor is this writing unimaginative in any sense; no seams of autobiographical experience are left showing, at any rate. Hadley's prose style is impressive because it never grates, cloys or strains, but it is also less distinctive for those same reasons.

The London Train is a novel of convalescence, in which its middle-aged characters are recovering from their parents' deaths, and this convalescence reveals to Cora that "to treasure up relics from every phase of her life as it passed, as if it were holy" was "a falsely consoling model of experience". Now she feels that the "present was always paramount, in a way that thrust you forward: empty, but also free".

This change in experiencing the flow of time is, in a way, the best defence for the author's refreshingly matter-of-fact approach to sexual infidelity. The lesser defence is, as in Hadley's previous work, the way relationships work themselves out via third parties  one meaning behind her allusions to The Golden Bowl. This is not The Golden Bowl, but it is a good read, with ideas as mature as its characters.

By far the most interesting feature of Tessa Hadley's carefully sculpted novel is the way she enters so completely into her characters' private worlds of thought and action. The minds of Paul and Cora, the male and female centres of the novel's two mirroring halves, are so fully occupied by this most astute and sympathetic of writers, that the reader hardly questions their weirdest and least wise moves.

Whether it is Paul, offering £2,000 cash in a brown envelope to the sister of his teenage daughter's unknown boyfriend, or Cora chucking in her whole life (job, husband, hopes of a baby) in favour of the solitude and blankness of doing up her dead parents' house in Cardiff, Hadley takes her reader inside their heads, so that we are drawn into a kind of understanding of their peculiar, dishonest ways.

Clueless, griefstricken Cora, on the run from everything and yet at moments sharply, excruciatingly in touch with herself, resembles one of Rachel Cusk's characters: knowing, intelligent, lost. "She saw herself at that moment as a tiny figure at a great distance, like an illumination in a manuscript: a naked female with little white, forked, vegetable legs, emblematic of the vanity of earthly delights," Hadley writes of Cora as her adventure with Paul spirals out of control.

Like Cusk, Hadley wrote her first novels about female characters, but as they have grown in confidence both have written more about men, and cheating, confused, disarming Paul is a triumph for Hadley, likeable and dislikeable at the same time.

Elliptically, in its second half, which is titled "Only Children", the novel tells the story of their affair, begun on the London train and ended in Cora's house. To Paul, married with two young daughters he adores, as well as teenage Pia from his first marriage, Cora quickly becomes "that girl in Cardiff", an indiscretion forgotten in the drama of Pia's pregnancy and an ominous falling-out with his wife. But to Cora, Paul is briefly everything, the thrillingly engorged centre of her lonely, desperate life. Their encounter is described beautifully as Cora watches it happen, keenly self-conscious yet not really in control: "He wasn't really listening to what she said, he was watching her: or, he saw what she said as if it was an attribute, part of her quality, not an idea separate from herself. She felt herself laid open in the bleaching light of his attention. What he liked, she understood, weren't her liberal ideas on education, but her hardness, which was personal and  newly, after the last two years  had something finished and ruthless in it. He was not taking advantage of her desperation; it met something in him, he reciprocated it. And also, of course, he was drawn by how she looked; he couldn't help it and she couldn't help drawing him after her. She began to feel herself enveloped in that rich oil of sex attraction, so that she moved more fluently, knew there was something gleaming and iridescent in how she turned her head away or smiled at him."

Both Paul and Cora have recently lost their mothers, both have marriages at risk of collapse, both have a friend of the same sex who is also linked to their spouse. Both work at the unglamorous edges of literary life  he as a critic, she a teacher and librarian  and move between London and Cardiff as if between different lives. There are other echoes and correspondences between the stories  ex-partners, children, loved ones going missing  but the overall effect is asymmetrical mainly because the affair itself is left to Cora's half of the book.

While full of admiration for her prose and psychological acuity, critics have sometimes chided Hadley for her lack of interest in plot, goading her in impatient reviews to make something happen to her characters, to shock them out of their emotionally rich everyday lives. The London Train does not meet this demand exactly. It covers themes familiar to Hadley's readers, and is interested above all in the relationships we have with others and ourselves. Paul's marriage to Elise stands out for its ambivalence, rooted in part in their feelings about class. "Does the meanness come from your background, did you get it from your parents? Are you jealous, of all the memories we have?" upper-middle-class Elise asks Paul, on the brink of relationship breakdown.

But from the mystery of Pia's pregnancy and strange new life in London, where Paul briefly joins her but from which her mother Annelies is shut out, and from the disappearance of Cora's ultra-reliable civil servant husband Robert, Hadley has crafted real excitement so that each story ends in a flurry of curiosity. In "Only Children" this is somewhat contrived, and Cora's story is strongest as a character piece. But The London Train snaps shut with an effective twist.