When, seven years ago, Andy Hamilton was making his television comedy series Bedtime, he cast his daughter Isobel in it. She was seven. Hamilton was struck by the impossibility of getting small children to behave convincingly on screen. For example, he points out, children tend to be shown standing still and delivering their lines with their eyes fixed on their adult interlocutor. In reality, small children are almost always playing with something, and tend to stare at anything but the adult — “who is invariably the least interesting thing in the room”.

Hamilton discussed the problem with the actor Kevin McNally, who at once came up with the solution: “Don’t let them see the script.” It worked.

Now it works even better. For Hamilton, along with his Drop the Dead Donkey collaborator Guy Jenkin, has used the simple device of denying children a script to produce Outnumbered, unquestionably the best British sitcom in years and among the best ever. As a portrait of a dysfunctional household redeemed by love and the acceptance of our fallibility, it bears comparison with The Simpsons. And, like The Simpsons, it consoles.

“People tell me,” Hamilton says, “that they’ve been reassured by the show. We get e-mails from viewers saying they’ve watched the show and felt better, because it shows other people cocking the same things up. We see it as a little bit of an antidote to the parenting industry. We’re saying being a crap parent is okay.”

Funny, poignant, occasionally harrowing and — the highest praise of all — true, Outnumbered is about a family, the Brockmans, consisting of two adults and three children, hence the title. It is set primarily within the cluttered confines of their suburban house. How this is done is crucial to understanding both the power of the show and the importance of its innovations.

The real house is in Wandsworth, southwest London, though it was chosen because it looks as though it could be anywhere. The team also uses the house next door as a green room and study area for the child actors. The law requires children working in film or television to have a tutor; they cannot be on set for more than 45 minutes at a time or more than three hours in any one day. This seems phenomenally restrictive, but Hamilton and Jenkin have turned it to their advantage.

One of the children, Jake (Tyger Drew-Honey), is 12, and is treated more or less as an adult. But Karen (Ramona Marquez) is seven and Ben (Daniel Roche) is nine, and these two are assiduously denied access to the script. Instead, when they come in from next door for their 45 minutes, they are taken aside — Ben by Hamilton and Karen by Jenkin. The two whisper in their ears a kind of mission statement for the scene they are about to shoot. The adult actors can’t hear this, and have only their lines. All then launch into the scene, doing perhaps two or three takes in the allotted time. Everything is constructed to allow for the unexpected, for what is most striking, bizarre and liberating about the child’s-eye view.

“Don’t work with children unless you want unpredictability,” says Hugh Dennis, who plays Pete Brockman, the dad. “We see Andy and Guy whispering to them and we have no idea what they are saying. We’ve been told to learn our script, but not terribly well. . . It makes you sort of realise that getting old is just suppressing things you really want to say. So, at the end of the 45 minutes, the kids say the thing you want to say, which is, ‘Do we have to do this again? Can’t we have some biscuits?’ ”

Precisely because of the unpredictability of the children, it is seldom known in advance how, in detail, scenes will end up. If a child comes up with a brilliant line or funny diversion, then, while the kids are on their break, the adults have to shoot material to put it in context. In this case, Hamilton and Jenkin stand, out of shot, where the children would be.

To make this work technically, the filming is as simple and flexible as possible. Everything is shot with two handheld cameras and the set is more or less uniformly lit, allowing the children to move freely without plunging into shadow. It’s all done to allow the children to be children — and the results are dazzling. Jenkin points out that, at the most basic level, it produces lines from the junior cast that could not have been written by an adult. “We wanted Ramona to say, ‘You smell like you’ve been to the pub.’ She actually said, ‘You smell of pub.’ It’s a small change, but it’s more like a child, and it’s funnier.”

It is a tribute to the quality of the show that one is dazzled not simply by a series of disconnected gags or smart lines — a common failing in British comedy — but by humour driven by character, as in the best American sitcoms, such as Frasier, Cheers and Seinfeld. Again, Hamilton and Jenkin handled this aspect of the show with immense care. In advance of the casting process, they had sketched out a few broad character traits for the children — a tendency to lie, anarchic behaviour, a hatred of vegetables, a love of awkward questions and so on — but did not specify which of the three would have each trait. In fact, they didn’t even specify the gender of the three children. They ended up with two boys and a girl because they were the best of the 80 or so contenders who were auditioned. Once they had the right children, allocating the traits was fairly straightforward.

The imagination and energy of Daniel Roche made him the obvious choice for the fibber and anarchist Ben. In the first series, the dad, Pete, a history teacher at a failing comprehensive, discovers that, thanks to Ben, he is variously known in the outside world as a confidant of the prime minister and an SAS-trained assassin. Pete and his wife, Sue (Claire Skinner), worry about this in a good, parenty sort of way. In a sharp and cutting twist, however, they are sucked into blaming Ben for their own lies. Ben, I confess, is my hero — indeed, my role model. In a scene in the first series, he gave me my biggest laugh. Denied a toy in a shop, he starts shouting “Stranger, stranger!” while pointing at his dad. It is what he is taught to do at school to identify abductors. “Come on, Ben,” Pete says, picking him up. “My name’s not Ben!” he shrieks.

The vegetable-hater and awkward questioner is Karen (“The face of an angel,” Hamilton says, “and the mind of a barrister”). She offers a solution to the family’s financial crisis — “I know how we can save money, by not buying broccoli!" — and claims an allergy to peas. The rumour that there is such an allergy has, says Pete, been quashed by the Pea Marketing Council.

Karen’s forensic questioning can reduce adults to impotent rage and agonised self-assessment. Her logic is impeccable, as is her re-creation, using soft toys, of a television show that seems to be a cross between The X Factor and How Do You Solve a Problem Like Maria? Andrew Lloyd Webber is played by the weirdest-looking toy. “A complete fluke,” Hamilton claims implausibly.

Meanwhile, Jake, the eldest, watches it all with the poignant introspectiveness of a boy about to leave his childhood behind. Though broadly co-operative, he is distant and guarded with his parents, in a way that foreshadows later, inevitable rifts. And he helps to keep the brats in check — “Dad, Dad. . . Ben and Karen are trying to bite each other.” Jake is a clear example of the way the dramatic quality of this show means it doesn’t need gags every 30 seconds to keep you watching.

Faced with all this — and the harrowing complication of a grandfather with Alzheimer’s — the adults are all more or less incompetent. Sue is constantly in a condition of crisis about her job, and the sink comprehensive at which Pete teaches is run by a vile, managerialist headmaster who makes him apologise for a supposedly racial insult to a fat Muslim boy. “He’s a history teacher,” Jenkin says, “at a time when history is not a valued subject, in a school that would clearly not get a very good Ofsted report. He’s a man who has lost any ambition, and he’s up against a headmaster who is full of jargon — against the modern world, really.”

“We wanted the parents,” Hamilton adds, “to experience that feeling when you have small kids — you feel you are running to stand still much of the time. They feel they still have aspirations and dreams, but they never get there.”

The particular cross Sue is obliged to bear is her sister Angela (Samantha Bond). She is a “free spirit”, that most weasely, self-indulgent and dangerous of self-definitions. It always means the same thing — “I will evade all obligations” — and Angela evades the obligations of family life, including looking after the stricken grandad. Then there are the next-door neighbours. They have three perfect children and a special box that they hand over to the Brockmans periodically. It contains all the things thrown over the fence, usually by Ben. Sue and Pete watch them in amazement, wondering how it is possible for any children anywhere to be so perfect.

Angela, the headmaster and the neighbours are representatives of a world outside the Brockman house. It is a nasty place — irresponsible, replete with malevolent “expertise” and savagely judgmental. It seems specifically designed to make Sue and Pete feel they have failed, and it turns their home into a fortress, a defensive position against outsiders.

This seems bleak because it is. The problems faced by the Brockmans are all intrinsically insoluble.

Alzheimer’s is incurable, the headmaster is a swine, Angela is irredeemably selfish, Ben will lie, Karen will expose your worst secrets and Jake will suffer agonies of which he will not speak. Of course it’s funny — very, very funny — but is it just laughter in the dark? No, because, in truth, this is a story of heroism.

“We wanted to make them heroic in a very small way,” Jenkin says. “Heroic in the way they keep stumbling on and trying to do their best and not quite getting there. They’re bombarded by books and television, by supernannies, all with the best advice that tells you you’re doing it wrong and everybody else is doing it right. And it just makes you feel worse. It’s a celebration of just kind of stumbling along.”

“The overall message,” Hamilton says, “is that they love each other. Most families are like that. They make loads of mistakes as parents in every episode. In the end, though, it doesn’t matter.”

Jenkin says that sitcoms are often the best definers of the mood of an age: Steptoe & Son caught the 1960s, Only Fools and Horses the 1980s and One Foot in the Grave the 1990s. Well, if he’s right, Outnumbered defines the Noughties, an age of fake expertise, “free” spirits, the decayed strictures of political correctness, bourgeois judgmentalism, marketing and, above all, uncertainty.

It is an age in which you make what you can of what you have, uncertain, afraid, but, with luck, in love.

Or, as Ben — my hero, the boy I wish I’d been — says when Karen gets locked in the toilet: “Put beavers through the window and they’ll eat the door.” Of course.

Outnumbered is on BBC1 on Saturdays at 9.10pm

www.bryanappleyard.com

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