The Terminator is back. Again. And again...

Hasta la vista, baby!" declared a certain former bodybuilder from Austria as he made the Terminator films one of history's most successful action-movie franchises, "I'll be back!" In the end, Arnold Schwarzenegger's political career got in the way of his promise to return yet again as a time-travelling assassin. But in spirit, at least, his monosyllabic catchphrase has come true: the fourth Terminator film comes out next May, while the second season of a spin-off TV show, The Sarah Connor Chronicles, will hit the UK's living rooms on Thursday night.

Both projects represent potential British triumphs. The eagerly awaited James Cameron film stars Pembrokeshire's finest action hero, Christian Bale. Its small-screen sibling, meanwhile, rests on the delicate shoulders of Yorkshire lass Lena Headey, of Remains of the Day fame, who is ably supported by the acting rookie Shirley Manson, the former lead singer of the Scottish rock band Garbage.

At this stage, a guilty secret: I've been obsessed with Terminator for years, and can barely contain my excitement at its return to cinemas. In the meantime, like all fans, I've been making do with the remarkably good Sarah Connor Chronicles, which has achieved extraordinary success on both sides of the Atlantic.

The idea behind the TV show is as follows: Sarah Connor (Headey) and her teenage son, John (Thomas Dekker), tour present-day America trying to avoid cyborg hitmen – "terminators" – who closely resemble humans, are nearly impossible to kill, and come from an apocalyptic future where machines rule the earth. They are helped in this mission by a "friendly" cyborg, played by Summer Glau.

This concept was developed from the first two Terminator films, in which John Connor is targeted for assassination because he will one day emerge as the leader of a revolutionary uprising by humans hoping to reclaim the world.

On paper, this may sound like the stuff of a ropey science fiction potboiler. Yet in the event, The Sarah Connor Chronicles turns out to be a strikingly thought-provoking drama. The show launched in the US in January this year, garnering rave reviews and securing a blockbuster audience of 18 million for its network premiere. Across the series, it averaged 12 million viewers, making it one of the most watched shows of its type in America. Around 40 per cent of its viewers are women – quite a distinction, considering that the audience for sci-fi is usually an 80-20 male/female split.

The show owes its success to two factors. Firstly, time travel has always represented a fertile stomping ground for an imaginative dramatist, raising trusty old questions about free will, fate, self-determination, and what have you. Secondly, Headey and Dekker's mother-son dynamic creates the sort of engaging human relation-ship that is missing from most contemporary science fiction.

British TV viewers seem to agree. When the first series of The Sarah Connor Chronicles debuted in the UK on Virgin1 a few months back, it drew almost 900,000 viewers, becoming the most watched show so far in the cable channel's short history.

The programme was the brainchild of Josh Friedman, who remains its head writer, and who recently took a break from filming the 13-episode second series to show me round his warehouse-sized sound set at Warner Brothers Studios in Los Angeles. Friedman was the man behind the 2006 thriller Snakes on a Plane, which overcame mixed reviews to earn double its $30m budget. He attributes much of the success of The Sarah Connor Chronicles to the strength of the underlying Terminator brand, combined with a plot that was drawn from an element of the drama that the original films skimmed over. "The mother-son relationship is really the primary relationship in the TV show," he says. "You can't do action all the time, and who wants to? What works in television is relationships. They did a nice job in the movies of depicting Sarah and John's relationship, but they didn't spend much time on it, and it's something I knew we could really delve into."

Throughout Sarah Connor, Friedman has insisted on high production values and state-of-the-art special effects. But the show's critical success has also revolved around its bleak, uncomfortable tone, which dovetails with the doomsday atmosphere of our times. Critics have lapped it up. "As much as audiences have fed their escapist impulses in recent years, they have also craved narratives of crisis and survivalism," wrote The New York Times. "These are bleak times after all. And there is no series on television right now bleaker, gloomier or more reflective of the depth of a certain kind of collective despondence."

The swift schedule of TV production makes for hectic working conditions, and Friedman's cast are on set up to 11 hours a day. Much of their time is spent covered in green masking tape (which allows special effects to be added later) or manhandling the waxwork models of themselves, which are used as props. Filming moves quickly between adjacent sets, which range from patches of fake desert to futuristic office complexes constructed from plywood.

"The great thing about our show is that it shows women in a powerful light," says Richard T Jones, who plays FBI agent James Ellison. "Usually, science fiction doesn't do that. But what we see in Sarah Connor is a strong woman, a woman of courage and bravery, and also someone who is not only strong-minded but strong physically. You don't see a lot of strong, physical women on TV, but she can take a punch and dish it out, and I think that's what has attracted women to it."

One strong woman bound to make headlines is Manson, who was invited to audition for the role of arch baddie Catherine Weaver as a result of her friendship with Friedman's wife. Her acting debut has, among other things, seen her character emerge (via special effects) from a men's urinal and murder a hapless bystander. "I have never done any professional acting, so it's been totally terrifying," she says. "Its very uncomfortable having to learn to do something in front of millions of people, and it took a conscious effort for me not to fall to pieces on set on the first day."

Manson credits at least some of Sarah Connor's success to the fact that technological progress has contributed to the Terminator franchise's relevance. "The concept of machines being about to take over the world has become much closer," she says. "In Japan they have robots that can do your shopping. Here we have iPhones and satnav, and rely so heavily on computers. We put a huge part of our lives into them, so somehow it seems even more real."

A recent immigrant to LA, Manson says the show provides a counterbalance to much of the bubbly drama and "incredibly conservative" content on US television. "I think this show is a little more subversive than your average TV show. It's darker than most shows. On network TV, people have had a bellyful of pretty pictures, and there's an appetite for everything that's frightening in the world. This projects a different world order, so I think it's a show for these particular times."

The new series of 'The Sarah Connor Chronicles' starts at 9pm on Thursday on Virgin1; 'Terminator Salvation' is due for release next year