The story spans billions of years, from the beginning of the universe to the ways in which it might end - though Professor Hawking says: "A few years ago when I was giving a lecture I was asked not to mention the end of the universe in case it depressed the stock market."
He does assure viewers that any cataclysm is a few billion years away at least. But he also squashes two of the favourite ideas of science fiction - time travel and friendly aliens.
Although many theorists now talk seriously about using "wormholes" formed by microscopic black holes to travel in time, Professor Hawking is dubious. "Why haven't we been visited by aliens or tourists from the future?" he says tersely. "Of course, some people would claim we have been visited, and that's what UFOs are. But I think any such contact would be much more obvious and probably very nasty."
The team producing the six, hour-long programmes travelled to 60 locations around the Earth and used computer graphics to take the viewer beyond the normal confines, in an attempt to expand the book's dense explanations.
They hope the programmes will do for the history of the universe what Lord Clarke's Civilization series did for the history of humans.
"For the book to be a public success people don't need to read it, just to buy it," says director Philip Martin. "But for this series to succeed, we have to get people to watch it."
Getting the scripts and the science right required lengthy consultations. Professor Hawking, holder of the Lucasian chair of mathematics at Cambridge, insisted on sanctioning all the detailed scripts. "He didn't want to do anything about being a brilliant mind in a crippled body," says David Filkin, the producer. Martin agrees: "He was keen that it should be about his ideas, rather than being a biography."
It was not the first meeting for Filkin and Professor Hawking. "Stephen and I were undergraduates together at Cambridge," he says. "We were in the rowing club. Well, I rowed and he coxed. He was an enthusiastic, determined cox - determined that we should row harder. He was a single-minded, determined person."
It seems little has changed in the 20 years since then. "It was the first time I had met him in his disabled state," Filkin recalls. "But he quickly put me at ease." Both men found Hawking, who has an electric wheelchair, a remarkable TV performer. "He always hit his marks," says Martin. "Everybody who worked with him was conscious of working with a great mind."