When Shia LaBeouf describes himself as ‘president of the lucky club’ he’s not kidding. Even by Hollywood standards, the 21-year-old’s rise has been meteoric.

Having shone as the child lead in 2003’s little-seen Holes LaBeouf spent the next four years providing plucky support to films like Constantine and I, Robot. Then, in 2007, came the sleeper success of Disturbia, the critical acclaim of A Guide to Recognizing Your Saints and the box office smash Transformers. Suddenly, LaBeouf was everywhere and he followed this by landing a plumb part in 2008’s most anticipated blockbuster, Indiana Jones & The Kingdom of The Crystal Skull.

Sitting before me in a plush London hotel, the star is clearly still trying to get his head around being on first name terms with legends such as Harrison Ford and Steven Spielberg. ‘I haven’t accepted any of this yet,’ he says candidly. ‘It all seems like the craziest thing in the world. I’m a kid from Echo Park and I shouldn’t be working with Steven. I mean, it’s wild when Steven becomes Steven. And “hey Harrison!” That’s crazy as well.’

‘My dad didn’t give a shit about movies, ever. He doesn’t care about any of this stuff, which helps to maintain normality. But then when I tell him something like, “We were training today and Harrison pulled out the whip and started doing whip training”. . . my dad went nuts!’

Very little is known about the fourth Indiana Jones adventure – the first since 1989’s Last Crusade – except for the fact that it’s set in 1957, at the height of the Cold War, and Professor Jones has fallen on hard times. LaBeouf plays Mutt, ‘a rebellious youngster’, who carries both a grudge against the archaeologist and a proposition for him that could lead to one of the biggest archaeological finds in history, the Crystal Skull of Akator.

Speaking of his larger-than-life co-star, LaBeouf is clearly in awe. ‘There’s stuff that Harrison’s doing that you wouldn’t believe they’re even letting him attempt,’ he laughs. ‘The stunt guys are so nervous, sitting there going: “Harrison, maybe not!” But he’s gung-ho about it, saying: “Don’t worry, I got it!”’

‘He’s a man’s man. He showed up for rehearsal and jumped out of this helicopter onto a motorcycle. And then there’s the whip training. Indy isn’t a big removal from Harrison for real. He’s a super hero. In his off-time he saves boy scouts. That’s what he does, so he is that guy. He’s doing stuff [at 65] I can’t do and I’m 21!’

Post Indy, LaBeouf’s star continues to rise with another leading role in action thriller Eagle Eye followed by the Transformers sequel. Not bad for a kid who got into acting as a means to an end; to support his mum, a former ballet dancer from New York, and dad, a French-Cajun former clown from San Francisco.

Commenting on where he sees himself in 30 years, though, LaBeouf is typically realistic: ‘Train conductor, bag man at the grocery store . . . that’s the stuff I dream about. I don’t go to bed at night and dream about these fantastic things that normal people dream of . . . I dream about real, normal shit such as fixing motorcycles because it’s just not accessible at this point.’

Indiana Jones & The Kingdom of The Crystal Skull is out on Thu 22 May.