The Rainbow Loom is a playground must-have that has made its inventor a mint

It is neither particularly hi-tech nor, at around £20, terribly expensive. Yet the Rainbow Loom has become the children's must-have item of the summer.

All 20 of the best-selling toys on Amazon at the moment are either looms or loom-related. Owners use the plastic contraptions to weave colourful elastic bands – which can be bought for as little as £1.99 for a pack of 1,800 – into bracelets, necklaces and bags. Or, indeed, whatever else takes their fancy; the US talk-show host Jimmy Kimmel recently appeared in an elaborately patterned suit made with Rainbow Looms.

"They're easy and fun and you can make anything," says Giulia Galli, an 11-year-old fan from London. "They don't make a mess and they keep you busy."

More than three million looms have been sold around the world. David Beckham, One Direction's Harry Styles and the Duchess of Cambridge have all been spotted wearing so-called "loom bands" around their wrists.

The toy is the brainchild of Cheong Choon Ng, a Malaysian-born, Michigan-based seatbelt designer. He created the original Rainbow Loom three years ago to impress his daughters, whom he'd seen weaving elastic bands over their fingers to make bracelets. When he'd tried to join in, his fingers were too large and clumsy. So, using a wooden board and a handful of pins, he built a primitive "loom".

It was his eldest daughter, Theresa, then 12, who suggested that her father market his creation. Unable to afford the cost of manufacturing in the United States, he spent $10,000 having the first batch made in China. They were shipped over to his home in parts; he and his wife assembled them in his living room.

Initial attempts to sell the results online were unsuccessful – but when Ng and his daughter began posting YouTube videos demonstrating how the loom worked, things turned around. In summer 2012, the Learning Express Toy Store, which has 130 franchises across America, placed an order for 24. Within two days, they sold out. In the past year, Ng has sold four million starter sets at £20 each.

Soon, retailers were clamouring to stock Ng's toy. He left his job at Nissan, hired a distribution warehouse near his home, relocated the assembly line from his living room to a factory in China, and began exporting around the world. Since then, they have become a word-of-mouth hit.

Bella Triggle, aged seven, from Purley, Surrey, says that she heard about the Rainbow Loom through friends: "They all make bracelets so I thought it would be a good idea, too."

In this, it is reminiscent of another recent playground fad: Silly Bandz. The malleable bands of rubber, which can be shaped into animals, letters and jewellery, prompted a comparable frenzy in 2010. They were created by an American concert promoter Robert Croak, who spotted plastic wristbands being sold by a designer in China, and began selling similar ones online in 2008.

Indeed, it may be the organic development of the craze which in part explains its success, says Professor Jeffrey Goldstein, founder of the International Toy Research Association: "Big companies sometimes try to engineer these things, but kids are aware when something is the result of a big marketing campaign."

He credits the social element of looming with turning the toys into must-haves: "Children can make the bands and trade them. They provide the opportunity to engage in a safe, simple, social activity."

Avowed loomer Molly Street, aged six, from London, agrees: "My friends and I all sit around in big circles making rings and bracelets, in different colours and combinations."

So will we tire of the looming craze? Undoubtedly, at some point – but for the moment, looms are here to stay.

John Lewis says that recent weeks have seen stronger sales than ever. John Baulch, publisher of Toy World magazine, believes this is a trend with longevity: "This is a great, good value toy – I can't see it disappearing this year."

Indeed, he may be right – not least because several schools have recently banned the looms following reports that they were causing playground fights. And if there's one thing that's guaranteed to fuel a children's fad, it's adult disapproval.