London's tech economy is booming as apps and games made there entertain the world – and experts predict the first global trillion-dollar company will rise in the UK, most likely in big data. What is the secret to this rapid success?

Near the tree trunk-shaped reception desk and the tubular slide, youngsters in skinny jeans perch among beanbags scattered on the Astroturf floor. Beneath a ceiling sprouting jungle foliage, the talk is all of apps and coding.

We are in the offices of one of the most successful children's games studios on the planet, but the location is not Silicon Valley; it is a back street in the London district of Hoxton.

"Mind Candy could be the next billion-dollar company coming out of London," says Mark Woulfe. A 22-year-old studying for his masters in computer games at Goldsmiths, he is on secondment to the British developer whose Moshi Monsters online playground has just passed 90 million subscribers. Woulfe is helping Mind Candy make games for mobile phones, where the most popular titles can attract more than a billion players and the financial rewards can be life-changing.

Last Thursday evening, as part of London Technology Week, he was talking to would-be developers about how to get into the trade. While many young Europeans are struggling to find work, those gathered in the Mind Candy offices that evening will be pushing at an open door.

The technology and information sector in London and the south-east is growing faster than in California, with 382,000 people working in computing, gaming, telecoms, film and media, according to a report by South Mountain Economics, published to mark London's technology jamboree. Include Oxford and Cambridge, and the numbers are bigger than California, with 744,000 workers.

In financial technology, economists say the capital employs as many people as New York. When it comes to games played on mobiles and tablets, Europe is already a bigger force than Silicon Valley, with the creators of Candy Crush, Angry Birds, Clash of Clans and Minecraft all hailing from Britain and the Nordic countries.

John Earner is an American games veteran who chose London rather than Silicon Valley as the location for his mobile gaming startup, Space Ape. Two years ago he left his management job at the publishing giant Electronic Arts to set up in Soho, from where he makes the phone and tablet game Samurai Siege.

"I thought about it for many months. I'm originally from San Francisco, so going back there, given it is the vortex of tech, makes a lot of sense on paper. But I chose to make a gaming company in London because it is easier to do and because the company would be better."

The quality of local talent was a big factor. Earner's co-founders are the former Mind Candy chief technology officer Toby Moore and former Skype executive Simon Hade.

London's ability to attract international workers is also a plus. Space Ape employs 50 people with 18 nationalities between them. "With the rise of the app store you don't get to choose your market any more," says Earner. "You make a product and the next thing you know there are people from 150 countries using it."

Down the road from Space Ape is King Digital Entertainment. With a head office in London and its main development hub in Sweden, King is one of the most successful products of the Anglo-Norse gaming scene. The company was valued at $7bn when it floated on the New York Stock Exchange earlier this year, and thanks to its sweetie-swapping hit Candy Crush, more people play King games each month than live in the US.

The money flowing into London's economy from the Apple and Android app stores is very real. This year an architectural puzzle game called Monument Valley, created by the Hoxton design studio ustwo, made back its development costs in one week, after topping the download charts. In just over a month, the game made £1.24m.

"In a lot of European countries, entrepreneurship is still frowned upon," says Rytis Vitkauskas, whose London startup YPlan is backed by the Hollywood actor Ashton Kutcher and American Express. "That attitude has changed dramatically in the UK. Young people now actually aspire to become entrepreneurs." YPlan sells tickets by answering the question "What shall I do tonight?" Started two years ago, it is already up and running in London, New York, Las Vegas and San Francisco.

A Harvard-educated Lithuanian who worked as a venture capitalist in London, Vitkauskas's globetrotting background is typical of the new generation of London tech entrepreneurs. Many, like his YPlan co-founder Viktoras Jucikas, whose previous job involved creating computer programmes for a Goldman Sachs trading desk, came to the UK to work in finance before branching out into something more fun.

Alongside digital entertainment, the capital has become a hub for big data – industry jargon for the art of organising the mass of internet-generated information into useful knowledge. In industries like banking and advertising, according to South Mountain Economics, London already has 54,000 big data workers. This compares to 57,000 in New York and 98,000 in San Francisco.

One of the UK's best known venture capitalists, Sherry Coutu, whose previous investments have included Lovefilm, believes the world's first trillion-dollar company will be in big data, and it will be British. The data it will use, says Coutu, is produced by the National Health Service. "If we use algorithms to analyse how patients get diseases, we will create a trillion-dollar company. I'm very optimistic that company is going to come out of London."

Controversially, the NHS has recently made patient records available, in anonymised form, to the private sector. Because the UK's health system is state-run, the information gathered by trusts is standardised, comparable and, therefore, extremely valuable to pharmaceutical firms. This is not the case in America, where healthcare is private and each hospital sorts data in a different way.

Entrepreneurs say London's tech boom owes much to government policy. Tax breaks that let film studios recoup one quarter of all money spent making films with British content using British actors and crews have doubled employment in the sector. This year chancellor George Osborne extended that help to games studios, and the impact on jobs is expected to be just as significant.

James Layfield, whose Central Working rents desk space in a club-like atmosphere to companies including Rovio, maker of Angry Birds, and Microsoft, for its east London-based startup incubator, says the Tech City initiative has also made a difference.

Launched in 2010, the government–funded body works to attract digital businesses to the UK, informs policy makers, and helps recruit talent by endorsing visas for foreign workers.

"The Tech City initiative was a massive piece of PR, but it was enough to catalyse something special," says Layfield. "We have seen a shift in the last few years in confidence and excitement, in a willingness to believe."