Mark Burnett remembers clearly his first army posting. He was 18, a youngster in the Parachute Regiment, patrolling the “bandit country” of Armagh. “We weren’t wandering round the streets of Belfast and Derry doing riot stuff – we were sneaking round the woods on intelligence, looking for things.” He says he and his colleagues were “working all the time, patrolling. You get shot if you’re sitting on your arse, taking it easy. There was almost a mutual respect with the IRA.”

Really? “Yeah. The day we left they sent a telegram. ‘You’re a good unit, you didn’t lose a man. But ours is a lifetime struggle. You were just here for five months.’”

Fast-forward a couple of decades to another lifetime, another deep-cover experience: Mark Burnett recalls the “eureka” moment when he came up with the idea for The Apprentice. By now a Los Angeles-based television producer, he was in the Amazon filming Survivor, the reality show in which “tribes” of contestants battle to make fires, catch fish and triumph over their fellow castaways, which the producer had turned into one of the most profitable programmes on American TV. Now, hunkered in the jungle, he watched a swarm of predator ants, working together for the good of their colony.

Burnett, who fires out ideas and deals with predatory zeal, wondered: what about a TV show – a competition – in which human endeavour was rewarded? What if this took place in the business world? In Manhattan, say, with a tycoon controlling the efforts of the worker ants? They would work together, but also against each other, trying to impress the boss. The ultimate reward would be a job by his side. The winner would be hired, the losers fired.

The first season of The Apprentice, with Donald Trump in the role of boss, premiered on American TV in spring 2004. The final attracted 28 million viewers. The genius of the idea, thinks Burnett, lies in its simplicity. “It’s a three-month televised job interview,” he says. “But instead of CVs you have actual tasks. That’s pretty universal – we all want jobs. We’ve all interviewed for a job.”

The UK version launched the following year. This time Sir Alan Sugar was the self-made millionaire telling contestants, “You’re fired!”, or handing down a job with a six-figure salary. It started in an unappetising slot: 5pm on BBC Two. But it became a word-of-mouth phenomenon. Last year’s third season was bumped up to BBC One; the viewership reached six million. The current season, which will reach its finale in three weeks, is loaded with that rare thing in an ever more fractured TV-watching environment: genuine “watercooler moments”.

“When I saw the US Apprentice, I thought, ‘What fantastic telly,’” says Michele Kurland, executive producer of The Apprentice and head of factual entertainment for talkbackTHAMES. “I’d been at the BBC business documentary unit and knew the challenge to humanise business people is a hard one. The programme does just that.”

For Burnett, the UK success is especially sweet. He’d triumphed in Hollywood with a raft of shows and a clutch of money-making partnerships: with Steven Spielberg on movie-making talent show On the Lot; with Sylvester Stallone and sports equipment manufacturer Everlast on boxing contest The Contender; with daytime-TV titan Martha Stewart, whose comeback Burnett masterminded after her imprisonment for lying about a stock trade in 2004. The same year, he was named by Time magazine as one of its 100 Most Influential People, recognition of his having introduced a new genre to American TV. But with the British Apprentice he was finally a ratings success at home.

I meet Burnett, 47, in the sprawling offices of Mark Burnett Productions, located by the 405 freeway to the west of Los Angeles. I’ve met him before, in 2005. Then, he estimated he had around 400 employees; he professes not to know how many there are now. He’s been resident in the US since 1982 – rather than return to the UK after leaving the Paras in the wake of the Falklands conflict, he opted to try his luck in California – but his accent is still pure Essex.

We sit in armchairs in his office. The room is filled with ethnic artefacts picked up while filming Survivor. There are wedding photos: he married for the second time last year, to Irish actress Roma Downey; between them they have three children. Last month’s Sunday Times Rich List put their joint worth at £120 million. On the wall are some of the certificates testifying to 48 Emmy Award nominations (he’s won two). He hands me a plaque honouring his induction last year into the Broadcast and Cable Hall of Fame. “What makes it particularly valuable to me is that I must be the first reality person inducted into it.

“It’s still amazing when you look back – in ’82 to have come here with a couple of hundred dollars, and find a way to fit in and succeed. It’s amazing,” he repeats, ever the good showman-salesman, even of himself. He’s written two memoirs that double as self-help books: the second was titled Jump In! (Even If You Don’t Know How to Swim), an update of the first, Dare to Succeed. He speaks in clipped, often ungrammatical sentences, but always with chutzpah. “I look around and often I’m the least formally educated person I know.”

Burnett credits his Hollywood success to his roots, “to a family upbringing in a working-class area like Dagenham, where you always had a good sense of humour”. He says he feels Scottish – his parents were Glaswegians who moved south to work on the Ford assembly line – but also that he grew up with an East Ender’s values. “That make-do spirit and ability to laugh at yourself. Added to the Parachute Regiment training, ready for anything. Overcome, adapt.”