Take 25 smiling faces, five dogs and one unrepeatable moment, captured for ever, guaranteed to still be being pored over 20, even 50, years from now. That's the family portrait; and the particular one in my mind right now was taken last week of a rather famous clan called Soames, to mark their mother's 90th birthday.

Mary Soames is the last surviving child of Winston Churchill: in the portrait she's seated centre, every inch the family matriarch, waving her arm to the camera in distinctly Winstonian fashion. Around her are ranged her colourful and interesting family. Her larger-than-life son Nicholas, the Tory MP, is seated to her left, in what looks like a clear signal that, after mum, he's the most important person in this line-up.

Behind them are Mary's other daughters and sons (Emma, Jeremy, Charlotte and Rupert) and ranged around them and in front of them, a whole raft of their children and grandchildren, and their pets. As in all the best family portraits, the snapper has caught the precise second in which everyone is looking happy and relaxed; and what's more, there are those little foibles that give you a sense of the characters (like the larger-than-life Nicholas, who appears to be laughing so uproariously that he's having to hold on to the sides of his chair to keep himself upright).

In this digital age, you might have thought the family portrait had had its day. It made its debut, after all, with the arrival of photography, more than a century and a half ago. Until then, the only families who had a visual record of themselves were the very wealthy, who paid painters to capture how they looked in oils on canvas. The galleries of Europe are stuffed with portraits of royals and noble families, portraits that sought to do exactly what the family portraits in your home or mine, or the Soames's seek to do, which is to mark a moment, to capture a generation, to freeze a frame that is significant, vital and meaningful, and to give it a life of its own, for ever (or for as long as the painting or photograph exists).

Photography put that desire within the reach of those of more modest means, and in no time at all, it had taken root. Victorian family line-ups were posed, formal affairs: you wore your best clothes, you stood in a certain way, you inclined your head just so and, click! The moment is still there, inside those photo albums you inherited from Great Aunt Mildred when she passed on two decades ago.

Fast forward to today, and the funny thing is how similar to its Victorian counterpart the current family portrait is. You book your date; you go to the photographer's studio, which these days is likely to be a whitewashed loft building in some trendy bit of the city. You choose your clothes with great care; sometimes you take along a few alternatives, in case you want to vary the shots. And then you pose, taking care to look as unposed as possible. Look, your photo screams, from your sitting-room wall (the current vogue is for pictures to be poster-sized and framed): we just happened to be rolling round together in a room with a pristine white floor and white walls, wearing our best-but-not-too-formal clothes, on a day when no one was trying to kill anyone else! How remarkable was that?

And therein lies one of the great secrets of the successful family portrait. The key person in making the whole thing possible is undoubtedly the photographer, and in far more ways than being the person who points the camera and presses the button. What makes the snapper so important is that, because he or she isn't one of you, you're all on your best behaviour.

Everyone does as they're told (no one ever does that for Dad, when he sets up his tripod and uses the time-delay switch); when the person with the camera says "look this way and smile", everyone does.

And when the photograph is taken, and a few years have gone by, how precious these family line-ups become. On my desk as I write is a photograph taken in 1998 on my mother's 60th birthday. My father, already looking slightly frail, is sitting centre-stage: my mother, more relaxed, is sitting next to him. Around them are ranged their four children and four grandchildren. It was a moment that can never be repeated: my father has now died, the children have grown up, new children have arrived. One of my brothers has a new wife, and the other has split up from the wife in the photo. Families, though the anchor of our lives for most of us, change all the time: and it's our family portraits that remind us of the way we were, almost to the point of proving to us that we once looked like that, that we once were that young, that we once had a father alive, that we once had a baby.

Family photographs unite the generations, too, in a tangible way. The other family portrait in my study is one of the most precious images I possess: it shows my grandmother, then in her late eighties, holding a tiny baby – my daughter Rosie, then a few weeks old. Flanking them are my father and me: four generations in one frame, an image that only had a lifespan of a few short months before my grandmother was gone. Just once, she held a great-granddaughter: her old lady's hands, cradling the pink new skin, symbolise the thread of the years, the passing of the baton from one generation to the next – and only the family portrait could capture the weight and poignancy of the moment.

Then there are the portraits that were never taken – and the hole they leave. We never did have a professional picture taken, in my family, of all six of us: and then suddenly it was too late, because my youngest sister was dead, aged not-quite four, and the opportunity to show that we were once that family was gone. I once visited a family where a child died and then another child had been born – as happened in my own family, in fact – and I was shown a photoshopped portrait of the family with both children, the dead child and the living child, sitting next to one another on the sofa. The mother seemed proud of it, comforted by it: an old tradition and modern technology had combined to give her a sliver of what life might have looked and felt like, had circumstances been different.

But there's another thing the family portrait does, and that is to create a narrative. I recently interviewed a woman in her eighties who had her family portraits lined up, six deep, on a huge table in the centre of her sitting room. The earliest portraits were of her grandmother and her parents in the late 19th century; the most recent were of her great-grandchildren and their parents. Through the images, she could trace her family history across seven generations: looking into those faces, some long dead, she could see similarities and resemblances and trace them through the years.

So it will be with the Soames family portrait, 20 or 30 years from now. Some as-yet-unborn young Soames will pick up the picture taken at his great-great grandmother's 90th birthday, and will idly muse on his great-uncle or his father's cousin's face and think: did he really ever look like that? He'll spot someone he doesn't recognise at all, and he'll find his granny to explain the lineage to him. And then he'll peer at his great-great grandmother, the one who had the very, very famous father, and he'll think: she was the link to him, the great wartime prime minister of the 20th century.

And while not every family has a figure like Winston Churchill in it, every family has history running through it: and every family portrait has its own rich, unique, and irreplaceable story to tell.