It is a Saturday afternoon, as we stand on the brink of pre-Christmas panic, and London is chokka with small people dragging larger ones in and out of toy emporia, driven on by a heady mixture of hunger, lust and greed.

The toy market always was a cut-throat one, manufacturers managing to target their audience with dastardly élan, and each year the emphasis appears to strive towards bigger, better, faster, more. But in one corner of the biggest toy emporium of them all, Hamleys, tradition is still rather quaintly observed.

The basement here is where Lego lives, has done for years now, and the little building blocks occupy an awful lot of floor space. The displays are lavish, the complicated train stations and cityscapes and traffic junctions all cluttered with those miniature versions of what always did appear to be Village People – pirates, cowboys, firemen... and is that a miner? Gathered around each display are families straining for a better view. The vast majority are boys and men, Lego is ostensibly a construction toy, and construction ostensibly, though not exclusively, a male pursuit. But the brand that has tried to engage girls before is in the process of doing so again. Marko Ilincic, its managing director for Britain and Ireland, promises that it will target girls successfully this time.

"It's all about getting the mixture of construction and fantasy just right," he says. "Fantasy, for girls, is the key."

But for now at least, it remains a boys' own world down here, the fascination for those colourful little building blocks covered in plastic warts exerting on the male imagination much the same influence it has for the past 75 years now. Lego, after all, is the world's favourite toy. And despite the ongoing financial crisis, it is booming. Every second, boast its makers, seven boxes of Lego are sold. This makes 62 bricks for every person in the world. That's a lot of bricks.

Little could Ole Kirk Christiansen, the founder of Lego, have known quite what he was creating back in the 1930s, when his only aim was to bring a smile to poor Danish children during the Great Depression.

Lego's story is one of endurance, and occasional necessary fortitude. Just seven years ago, for example, in 2003, the company was facing bankruptcy. The reasons, Ilincic says, were myriad.

"We had been a toy company for 70 years, but we seemed to forget that for a while," he says, specifying that they had begun to expand into other areas, theme parks for one, but also into the production of shoes and watches. "We lost our focus, what forms the heart of our core appeal. We had to find it again."

They did just that. Ridding themselves of many of their assets, including the theme parks, and carefully extending into the world of licensing (Lego now makes Star Wars and Harry Potter figurines, but nothing army-related; they prefer to perpetuate childhood innocence, not destroy it), the company got back, Ilincic says, to what they did best: "Making brightly colour building blocks." Its foundations were so humble as to be whimsical, the stuff of fairy tales.

For the first couple of decades, it prospered modestly, but it wasn't until 1958, under the direction of an incoming vice-president, that it happened upon the stubs-and-tubes mechanism that enabled one block to attach itself to another, and to another and another.

It really took off and by 1962 had expanded right across Europe, and into America. Six years later, it opened its first Legoland in Denmark, and in its first year welcomed over 600,000 visitors to Billund.

By the 1980s and 90s, much to its makers' glee, Lego's appeal had become genuinely pan-generational, the one toy that most adults chose never to get rid of, and promptly rescuing it from their parents' lofts the moment they became parents themselves. After reporting crippling losses of £144m in January 2004, its company rethink turned around and promptly doubled their fortunes, which is why today, in a world otherwise dominated by the likes of Xbox and Wii, the little brick that could still reigns so impressively supreme. Of the Top 20 Amazon toys right now, Lego occupies seven places. You could, this Christmas, buy a Lego-licensed digital camera, while Selfridges has developed a line in Lego jewellery. The company has also launched its very own board game, but being Lego, you have to build it yourself. You even have to build the dice.

So what is its secret, and why do we keep returning to this most basic of toys?

According to Charlotte Simonsen, company spokesperson at their Billund HQ, the building block continues to thrive because it offers so much more scope than its competitors. There is little that is instantaneous about it. Instead, it requires time and patience, a little vision, and, afterwards, a lot of satisfaction. It is also, she claims, psychologically speaking, brain food.

"It is one of the few toys that stimulates both the left and right sides of the brain," Simonsen says. "It makes us call upon our logic and engineering skills, while also allowing us to be creative and imaginative. There is quite a strict structure to Lego, but then again there isn't, you can do whatever you wish with it. It feeds the imagination."

And feeding the imagination, says Ilincic, "is the key to the brand. Children have a wonderful imagination, but too many toys today offer only instant gratification. We want to nurture their attention spans, not limit them."

It works wonders as a rehabilitative exercise too. While recuperating from his devastating car crash during the filming of Top Gear back in 2006, presenter Richard Hammond reportedly played with Lego during his convalescence, the building bricks helping him to redevelop spatial awareness and concentration.

Each year Lego's globally-based designers are required to produce at least 60% brand-new product.

"Our designers," says Ilincic, "even stay with families during the research process, often for days at a time. Children have far less free time these days. There is more pressure for them to perform at school, more emphasis on extracurricular activities. This is all very useful to know."

As is current fad and fashion. Increasingly, children these days seem to prefer a virtual world to the real one, which is why last year the brand launched something called Lego Universe. This is an online game in which individuals around the world can build bricks together on their computers. It is already fearsomely popular.

Back at Hamleys, there is a bottleneck at the bottom of the stairs, people lining up to have their photograph taken alongside a life-size model of Buzz Lightyear. Nearby are piled a great many boxes of Lego's City Airport, which was recently voted as one of the top Christmas toys this year, despite a look-twice price tag of £100. Right now, a little boy of about seven is eyeing it with palpable enthusiasm. But look just beyond him, and up into the eyes of his father. Behind a pair of glasses, they are sparkling.

This, for Lego, is pertinent. The father is the one with the wallet.