"They call me Fearless Felix," says the man who, with nonchalant courage, fell to earth faster than the speed of sound. Less than three weeks ago, Felix Baumgartner reached an altitude of 128,100 feet in a small capsule attached to a helium balloon before he plummeted back down again through 24 miles of cold blackness at a top speed of 833.9 miles per hour.

His space jump was watched live on YouTube by more than eight million people, and the fevered reaction online was matched by saturation coverage in the traditional media. As a curiously driven man, who had dreamed of flying ever since he was a five-year-old boy in Austria, drawing detailed pictures of himself soaring through the sky, Baumgartner had achieved his greatest ambition. He had moved from the often-illegal activity of base-jumping – having blagged his way past lax security at some of the world tallest buildings so his daredevil talents could be noticed – and become one of the world's most celebrated men.

Baumgartner sits in a plush chair in a London hotel and arches a wry eyebrow at his cartoonish nickname. "You and I know Fearless Felix doesn't really exist," he says, quietly, and more thoughtfully than might be expected. "He might seem like a cool guy, but I've had to address a real psychological battle. It's been way harder than stepping out into space."

He may be a certified celebrity, with an American twang to his Austrian accent, but he talks with the zeal of an ordinary man who has just survived an extraordinary experience. Baumgartner also uses the very human confines of psychological frailty, rather than the vast expanse of space, to frame his achievement. A canny publicist, the 43-year-old is smart enough to recognise that there is real strength in admitting moments of weakness. But there is also something surprisingly moving in his revelations that the source of his suffocating fear was an old-fashioned spacesuit.

"I feared and hated the suit because of my desire for freedom. I started skydiving because I loved the idea of freedom. But you get trapped in a spacesuit, and people are adding weights to it every day.