On 26 December 2004, when the tsunami broke across the shores of the Indian Ocean, killing at least 275,000 people in a dozen countries, my three small children and I were paddling in the sea in Bombay. We all noticed an unusually high, strong rip tide that morning, but it was not until we returned to the hotel that we learned how lucky we had been. We had changed our Christmas plans at the last minute to attend a friend's navjot  a Parsi ceremony akin to a confirmation or bar mitzvah  and so narrowly missed spending Christmas in a beach resort south of Chennai. That morning, the resort was completely devastated by the tsunami. Almost everyone staying there was either severely injured or killed.

Like millions of others, we sat watching the television pictures of the tsunami engulfing beaches and islands across the region, appalled and thankful that we had chosen the west rather than the east coast of India for our holiday. But it is only now, reading Sonali Deraniyagala's memoir, Wave, that I can even begin to understand the full horror of what happened.

That morning, Deraniyagala and her husband, parents and two boys were, like us, on a family holiday; but in their case they were 600 miles to the south, at the Yala national park, on the south-east coast of Sri Lanka. The first thing Deraniyagala saw was the sea rising  a sight that looked odd, but not threatening. Only gradually did the full import of what was happening dawn on her  "Oh my God," she screamed, "the sea's coming in." She grabbed her children and ran with her husband behind the hotel and into a waiting jeep. They were driving away when the wave hit.

Deraniyagala suffered an internal injury as the jeep turned over, and when she regained consciousness she was spinning around and around, bleeding, naked from the waist down, covered with mud, and with her mouth full of sand. She was quite alone. There was no sign of the rest of her family. For a while there was a strange calm: "I was floating on my back. A flock of storks was flying above me." Then she saw a child floating towards her, a boy, clinging to the broken seat of a car. For a moment she thought it could be one of her sons, but she realised as the child was swept past that she was mistaken: "I stared into this unknown landscape, still wondering if I was dreaming, but fearing, almost knowing, I was not."

The most moving passages in this extraordinarily moving book are in the section that follows: Deraniyagala is rescued and it becomes clearer with every passing minute that she is the only survivor of her entire family. With bleak clarity, and managing somehow to resist sentimentality, she recalls her thoughts as the realisation dawns on her that her entire world has come to an end. The restraint of her prose, with its short, simple declarative sentences, makes the scale of the horror all the more unbearable: "Someone suggested I take a sleeping pill. I refused the pill. If I sleep now I will forget. I will forget what happened. I will wake believing everything is fine. I will reach for Steve, I will wait for my boys. Then I will remember. And that will be too awful. That I must not risk."

As she is taken away to her aunt's house in Colombo, she writes of her quiet determination to end her life, huddling beneath the covers of her cousin's bed, hoarding sleeping pills, stabbing herself with a butter knife and "smashing my head on the sharp corner of the wooden headboard of the bed". She continually surfs the internet to find painless ways of killing herself. "I needed to know how to do it successfully, I couldn't mess it up."

For months, anything to do with children  toys, a cricket ball, the sound of small running feet  brings back the horror in overwhelming floods of grief. She begins drinking and experiments with mixing vodka and antidepressants. There are periods of pure madness. When her brother sells her Colombo house, she stalks the Dutch family that has moved in: "Strangers in our home. It's ghastly. The Dutch family, settling in there like nothing has happened. They must be dancing around in their fucking clogs." She drives there night after night, repeatedly ringing the doorbell at 2am, blaring the horn and blasting out her husband's favourite Smiths songs on the car stereo: "Asleep are we? Not for long, you won't be." On another occasion, she sees a bed where she and her husband and children had once slept, and finds a wicket that her sons had used to play cricket: "I struck at the bed. I stabbed the mattress with the muddied pointed end, over and over, harder and harder, until a tear appeared, and again to make the hole deeper and again to make another gash and again to join up all the gashes."

Slowly, she finds the strength to carry on. On one occasion she drags a friend on a crazy drunken expedition to see a place where turtles come ashore to lay their eggs. "It's Friday night," the friend barks eventually. "I could be in London, I could be down the pub. What am I doing on a godforsaken beach looking up a turtle's arse."

She visits and revisits the site of the hotel where she was staying when the wave struck. Once, her father-in-law finds fluttering at his feet a laminated A4 page from the research report her husband was writing when he was killed. "Except for a small tear in the middle, this page was intact. It had survived the wave? And the monsoon in the months after? I clasped the paper to my chest and sobbed." She finally stops her search when she finds her son's shirt "under a spiky bush, half-buried in sand. One of the sleeves was still rolled up."

It is two years before she can bear to return to the family home in London. Even then she can't live there, but after finding her husband's eyelash on a pillow and a dish with the remains of a beef curry he had cooked, decides instead to keep it as a shrine, unchanged in any way from how it was when the family set off to Terminal 4 to fly to Sri Lanka. Seven years later, "their absence has expanded ... Seven years on, it is distilled, my loss." The scale of her tragedy is so overwhelming that "it still seems far-fetched, my story, even to me. Everyone vanishing in an instant, my spinning out from that mud, what is this, some kind of myth?"

This is possibly the most moving book I have ever read about grief, but it is also a very, very fine book about love. For grief is the black hole that is left in our lives when we lose someone irreplaceable  a child, a parent, a lover. It is the negative image that, in its blackness, sometimes reveals love with a greater clarity than its positive counterpart. And while in Wave love reveals itself by the bleak intensity of the pain of absolute, irreplaceable loss, it is in the end a love story, and a book about the importance of love.

A grief like that suffered by Deraniyagala can have no resolution, but all books must end, and this one does on a pitch-perfect note of elegiac sadness and something close to acceptance, as she sits in anonymous exile in New York, "like I'm in a witness protection scheme", remembering happier times: the moment her son called her not by her own name but by that of her husband  "Mummy Lissenburgh"  as if she had "no identity without these three boys ... Steve enjoyed our son's account of me, of course. He egged him on. 'Clever boy, Mal, spot on, you're exactly right. You tell it like it is.' So, 'Mummy Lissenburgh!' Malli would chant. And the three silly boys would fall about laughing. Now I sit in this garden in New York, and I hear them, jubilant, gleeful on our lawn."

 William Dalrymple's Return of a King: the Battle for Afghanistan 1839-42 is published by Bloomsbury.