There are three self-portraits of Linda McCartney in the retrospective of her work opening tomorrow at the James Hyman Gallery in Savile Row. The 25 other photographs show us for the first time the impressive range of her black-and-white work and give us glimpses of the private world of the McCartney clan, the rock stars she photographed in the 1960s and the artists and friends whose company she and Paul enjoyed.

If you go along to this exhibition expecting to find the mediocre work of the wife of a rock star you'll be surprised - here McCartney emerges as a dedicated, accomplished photographer.

One of the self-portraits overshadows the whole lot. Taken in late 1997, a few months before she died, Linda is seen standing in the background of a mirrored reflection, her slim, slightly blurred figure is dressed in black, her hair is short, and her face staring calmly forward into the lens. Visible in the foreground is an empty sofa, a cast of William Blake's death mask and a crack in the mirror's surface that has been patched up with Sellotape.

The picture was taken in Francis Bacon's bedroom in the studio where he had lived and worked up until his death in 1992. On the day it was taken, McCartney had spent some time there with her children, larking about, exploring the paint-spattered spaces in which he had worked. At some point, she must have crept away on her own into his bedroom and set up this shot. The symbolism of death is everywhere, and Linda is in among it, still there but only just.

The picture hits very hard and Hyman has wisely given it a wall to itself because it doesn't sit easily among her other photographs. The rest of the exhibition shows the world through Linda's lens as a place composed of antics and ideas, musicians and children, coquetry, romance, languor and dreams. Hers was a world in which she found amusing suspensions of gravity and an abundance of human beauty, her perception of it now and again touching, now and again amusing, in an elegiac sort of way.

Her earliest work was portraits of rock stars taken in the 1960s, when she worked as a photographer for Rolling Stone magazine. These are the pictures that she was known for (as Linda Eastman) before she met Paul. Now 40 years old, they have gained force with the years, having history in tow, in the clothes, the poses and the attitudes. There is Janis Joplin looking almost Victorian in a black ruffle-necked blouse; and Mick Jagger in a striped blazer, turning towards Linda, his face half visible between parted curtains.

These were the counter-culture heroes, men and women who had a stake in looking scandalous, deadbeat and bizarre. But when Linda took their photographs she made them look normal - people rather like us, worried perhaps about their greying hair, their ageing parents. Simon and Garfunkel are seen rehearsing in 1966, singing at each other (they could equally be yelling at each other) before a background of microphones arranged like a cluster of clashing swords. John Lennon is captured during a rehearsal, his face turning to see something out of the frame, his face etched with worry.

Linda McCartney grew up in New York, the daughter of a powerful lawyer who represented William de Kooning among other clients. On the walls of her childhood home hung works by Picasso, Matisse, de Kooning, the Inpressionists. As a young woman she had studied art history, and her photographic influences were shaped when she visited the hugely influential photographic exhibition The Family of Man in New York in 1955. As Paul McCartney writes in the introduction to the exhibition catalogue: “She loved Stieglitz, Diane Arbus, Dorothea Lange, Walker Evans, Cartier-Bresson. She was very into Magnum photographers and into Edward Curtis and Robert Frank. I think she saw herself as following in their footsteps, photographing moments in time.”

On the evidence of this show, McCartney was consistent in the highly structured format of her work. A number of her photographs are composed around railings or bars and grids. Gilbert and George, for example, are imprisoned with each other behind the railing bars of their East London patio garden. There's the beautiful, tender image of her daughter Stella, photographed in Tokyo in reflection in a high-rise window, a complex image of railings and grids superimposed with Stella's face and Linda's shadow, framed with the waxy purity of a white orchid.

Her mature work dealt, at least subliminally, with the large and small ploys that human beings devise to create families that will work together with coherence and tenderness. There is Stella again, photographed in Monserrat in 1981, standing against a wall covered with comical posters introducing the concept of birth control. And there is the much reproduced 1982 image of the family in Scotland, Paul standing balancing on a fence in his dressing gown, Stella playing on the ground and James captured in mid-air leaping down from the bonnet of the Land Rover.

How light and warm the life in these pictures is. Her subjects know her and trust her enough to let their vulnerabilities slip out. Paul, photographed in Venice, sits in a pose reminiscent of Rodin's The Thinker, staring contemplatively out at the passing crowds, his reflection visible in the window on the other side of the frame. But the focus is on the elaborately decorated iron grill in the centre of the picture through which Paul looks out at the people, a nice inversion of the normal state of affairs in which the people were usually seen looking at Paul.

“Family photographs were private,” Paul writes. “All the family knew that we were being photographed for possible future use, but what was more in our minds was that she was documenting our family life.”

She also documented street life. Her photograph Old Men, Scotland 1968, shows a group of men in overcoats and flat caps standing against a wall, staring at one of their party huffing off down the road, hands in pockets and shoulders hunched. It could be a photograph from Picture Post. Like all street photographers, McCartney shows us the improbable conjunctions and balletic choreography of everyday life.

Her style depended on surface components, on composition (she apparently never cropped her work) and contrast, on aesthetics, sometimes on gimmicks. It was occasionally derivative of Cartier-Bresson's, and there are bright shafts of the work of Kertesz, of Imogen Cunningham and Robert Frank. But McCartney managed to ring enough changes on these masters to make the style her own.

Her compositions are pulled taut by a sense of unexpectedly active space, seen most evidently in the Scottish leaping-child photograph. People move through the picture plane, assuming positions that are separated yet oddly interconnected, so that they look like actors in tableaux vivants.

McCartney let her style droop when it came to animals, however. The Horses in Snow, Sussex, 1986, taken at their farm, shows a group of four horses prancing about in snow, their bodies dappled by falling snowflakes. It is an impossibly romantic image, too syrupy for inclusion here. Much more powerful, and with its own poignancy, is Balloon Stairs, 1984, a tightly structured image of a domestic staircase on which sits a scattered collection of balloons, presumably left abandoned at the end of a party.

Being married to Paul McCartney obviously contributed to Linda's profile, explaining her affinities, her sympathies, her access. We glimpse her heart as well as her brain in these images, but as a whole we see the consistency of an artist's particular eye.

Linda McCartney Photographs is at James Hyman Gallery, London W1 (020-7494 3857, www.jameshymangallery.com), from tomorrow to June 7

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